Details

analyze557.0ms (17.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
14%	85.8%	0.1%	7
22.6%	77.2%	0.1%	8
23.8%	74.5%	1.7%	9
40%	56.4%	3.7%	10
46.9%	48.7%	4.4%	11
48%	45.8%	6.2%	12
58.1%	32.2%	9.7%	13
62.1%	27.2%	10.6%	14

Compiler

Compiled 13 to 9 computations (30.8% saved)

sample961.0ms (29.8%)

Results

839.0ms	8256×	body	128	valid
107.0ms	1072×	body	128	invalid

Compiler

Compiled 26 to 18 computations (30.8% saved)

preprocess34.0ms (1.1%)

Algorithm

2×	egg-herbie

Rules

830×	`fma-def_binary64`
737×	`times-frac_binary64`
438×	`distribute-rgt-in_binary64`
262×	`div-sub_binary64`
251×	`fma-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	52
1	75	44
2	183	44
3	723	44
4	2221	44
0	3	3

Stop Event

1×	saturated
1×	node limit

Compiler

Compiled 12 to 8 computations (33.3% saved)

simplify28.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

527×	`fma-neg_binary64`
407×	`fma-def_binary64`
279×	`cancel-sign-sub-inv_binary64`
251×	`times-frac_binary64`
245×	`div-sub_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	25	11
2	56	11
3	175	11
4	443	11
5	1025	11
6	2797	11

Stop Event

1×	node limit

Counts

1 → 2

prune3.0ms (0.1%)

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

3.3b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	3.3b	(-.f64 (/.f64 (fma.f64 x y x) z) x)
	9.9b	(/.f64 (*.f64 x (+.f64 (-.f64 y z) 1)) z)

Compiler

Compiled 66 to 39 computations (40.9% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (/.f64 (fma.f64 x y x) z) x)
✓	3.2b	(/.f64 (fma.f64 x y x) z)

series26.0ms (0.8%)

Counts

2 → 72

Calls

18 calls:

2.0ms	(/.f64 (fma.f64 x y x) z)	y	inf
2.0ms	(-.f64 (/.f64 (fma.f64 x y x) z) x)	x	-inf
2.0ms	(-.f64 (/.f64 (fma.f64 x y x) z) x)	x	inf
2.0ms	(/.f64 (fma.f64 x y x) z)	x	-inf
2.0ms	(/.f64 (fma.f64 x y x) z)	x	inf

rewrite59.0ms (1.8%)

Algorithm

1×	batch-egg-rewrite

Rules

869×	`expm1-log1p-u_binary64`
664×	`prod-diff_binary64`
137×	`egg-rr`
83×	`add-sqr-sqrt_binary64`
79×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	19
1	156	19
2	2253	19

Stop Event

1×	node limit

Counts

2 → 137

simplify72.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

597×	`fma-def_binary64`
574×	`fma-neg_binary64`
201×	`distribute-rgt-in_binary64`
173×	`distribute-lft-in_binary64`
128×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	26	797
1	63	797
2	127	797
3	388	647
4	1148	647
5	2040	647
6	3179	647
7	3669	647
8	3702	647
9	3710	647
10	3710	647

Stop Event

1×

saturated

Counts

209 → 151

prune98.0ms (3%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	145	6	151
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	147	6	153

Error

0.0b

Counts

153 → 6

Alt Table

Status	Error	Program
▶	3.2b	(*.f64 (-.f64 (+.f64 (/.f64 y z) (/.f64 1 z)) 1) x)
	16.3b	(-.f64 (*.f64 y (/.f64 x z)) x)
	3.3b	(-.f64 (+.f64 (/.f64 (*.f64 y x) z) (/.f64 x z)) x)
	3.6b	(-.f64 (pow.f64 (/.f64 z (fma.f64 x y x)) -1) x)
	4.0b	(-.f64 (pow.f64 (cbrt.f64 (/.f64 (fma.f64 x y x) z)) 3) x)
	3.4b	(-.f64 (*.f64 (fma.f64 x y x) (/.f64 1 z)) x)

Compiler

Compiled 2977 to 911 computations (69.4% saved)

localize7.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (/.f64 y z) (/.f64 1 z))
✓	3.0b	(*.f64 (-.f64 (+.f64 (/.f64 y z) (/.f64 1 z)) 1) x)

series28.0ms (0.9%)

Counts

2 → 39

Calls

15 calls:

4.0ms	(*.f64 (-.f64 (+.f64 (/.f64 y z) (/.f64 1 z)) 1) x)	x	inf
4.0ms	(+.f64 (/.f64 y z) (/.f64 1 z))	y	-inf
4.0ms	(*.f64 (-.f64 (+.f64 (/.f64 y z) (/.f64 1 z)) 1) x)	x	-inf
3.0ms	(*.f64 (-.f64 (+.f64 (/.f64 y z) (/.f64 1 z)) 1) x)	y	inf
3.0ms	(*.f64 (-.f64 (+.f64 (/.f64 y z) (/.f64 1 z)) 1) x)	x	0

rewrite61.0ms (1.9%)

Algorithm

1×	batch-egg-rewrite

Rules

538×	`fma-def_binary64`
331×	`fma-neg_binary64`
199×	`log1p-udef_binary64`
198×	`expm1-udef_binary64`
116×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	10	26
1	227	26
2	3423	24

Stop Event

1×	node limit

Counts

2 → 110

simplify58.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

962×	`fma-def_binary64`
565×	`fma-neg_binary64`
175×	`cancel-sign-sub-inv_binary64`
113×	`distribute-rgt-neg-in_binary64`
90×	`associate-/l*_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	20	424
1	37	424
2	62	383
3	106	329
4	260	329
5	640	329
6	1295	329
7	2200	329
8	2936	329
9	3208	329
10	3224	329
11	3224	329

Stop Event

1×

saturated

Counts

149 → 124

prune106.0ms (3.3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	123	1	124
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	123	7	130

Error

Counts

130 → 7

Alt Table

Status	Error	Program
✓	3.2b	(*.f64 (-.f64 (+.f64 (/.f64 y z) (/.f64 1 z)) 1) x)
	16.3b	(-.f64 (*.f64 y (/.f64 x z)) x)
▶	3.3b	(-.f64 (+.f64 (/.f64 (*.f64 y x) z) (/.f64 x z)) x)
	3.6b	(-.f64 (pow.f64 (/.f64 z (fma.f64 x y x)) -1) x)
	4.0b	(-.f64 (pow.f64 (cbrt.f64 (/.f64 (fma.f64 x y x) z)) 3) x)
	16.4b	(*.f64 (-.f64 (-.f64 (/.f64 (pow.f64 (/.f64 y z) 2) (/.f64 (-.f64 y 1) z)) (/.f64 (pow.f64 z -2) (/.f64 (-.f64 y 1) z))) 1) x)
	3.4b	(-.f64 (*.f64 (fma.f64 x y x) (/.f64 1 z)) x)

Compiler

Compiled 2145 to 1284 computations (40.1% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (+.f64 (/.f64 (*.f64 y x) z) (/.f64 x z)) x)
✓	0.0b	(+.f64 (/.f64 (*.f64 y x) z) (/.f64 x z))
✓	6.5b	(/.f64 (*.f64 y x) z)

series42.0ms (1.3%)

Counts

3 → 45

Calls

27 calls:

4.0ms	(+.f64 (/.f64 (*.f64 y x) z) (/.f64 x z))	x	-inf
3.0ms	(-.f64 (+.f64 (/.f64 (*.f64 y x) z) (/.f64 x z)) x)	x	-inf
3.0ms	(-.f64 (+.f64 (/.f64 (*.f64 y x) z) (/.f64 x z)) x)	x	inf
2.0ms	(-.f64 (+.f64 (/.f64 (*.f64 y x) z) (/.f64 x z)) x)	x	0
2.0ms	(+.f64 (/.f64 (*.f64 y x) z) (/.f64 x z))	x	inf

rewrite89.0ms (2.7%)

Algorithm

1×	batch-egg-rewrite

Rules

862×	`fma-def_binary64`
420×	`fma-neg_binary64`
307×	`egg-rr`
208×	`expm1-udef_binary64`
208×	`log1p-udef_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	9	36
1	215	36
2	3652	32

Stop Event

1×	node limit

Counts

3 → 307

simplify56.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

876×	`fma-def_binary64`
549×	`fma-neg_binary64`
150×	`distribute-rgt-in_binary64`
123×	`distribute-lft-in_binary64`
118×	`unsub-neg_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	22	562
1	49	562
2	110	488
3	268	488
4	863	377
5	1740	377
6	2771	377
7	3478	377
8	3603	377
9	3603	377

Stop Event

1×

saturated

Counts

352 → 319

prune254.0ms (7.9%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	318	1	319
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	319	7	326

Error

Counts

326 → 7

Alt Table

Status	Error	Program
✓	3.2b	(*.f64 (-.f64 (+.f64 (/.f64 y z) (/.f64 1 z)) 1) x)
▶	1.6b	(-.f64 (fma.f64 y (/.f64 x z) (/.f64 x z)) x)
✓	3.3b	(-.f64 (+.f64 (/.f64 (*.f64 y x) z) (/.f64 x z)) x)
	3.6b	(-.f64 (pow.f64 (/.f64 z (fma.f64 x y x)) -1) x)
	4.0b	(-.f64 (pow.f64 (cbrt.f64 (/.f64 (fma.f64 x y x) z)) 3) x)
	16.4b	(*.f64 (-.f64 (-.f64 (/.f64 (pow.f64 (/.f64 y z) 2) (/.f64 (-.f64 y 1) z)) (/.f64 (pow.f64 z -2) (/.f64 (-.f64 y 1) z))) 1) x)
	3.4b	(-.f64 (*.f64 (fma.f64 x y x) (/.f64 1 z)) x)

Compiler

Compiled 5997 to 2163 computations (63.9% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (fma.f64 y (/.f64 x z) (/.f64 x z)) x)
✓	2.6b	(fma.f64 y (/.f64 x z) (/.f64 x z))

series35.0ms (1.1%)

Counts

2 → 72

Calls

18 calls:

4.0ms	(-.f64 (fma.f64 y (/.f64 x z) (/.f64 x z)) x)	x	-inf
4.0ms	(fma.f64 y (/.f64 x z) (/.f64 x z))	x	0
3.0ms	(-.f64 (fma.f64 y (/.f64 x z) (/.f64 x z)) x)	x	inf
3.0ms	(fma.f64 y (/.f64 x z) (/.f64 x z))	x	-inf
2.0ms	(fma.f64 y (/.f64 x z) (/.f64 x z))	x	inf

rewrite50.0ms (1.6%)

Algorithm

1×	batch-egg-rewrite

Rules

854×	`expm1-log1p-u_binary64`
695×	`prod-diff_binary64`
86×	`egg-rr`
82×	`add-sqr-sqrt_binary64`
78×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	7	25
1	155	23
2	2215	23

Stop Event

1×	node limit

Counts

2 → 86

simplify63.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

829×	`fma-def_binary64`
565×	`fma-neg_binary64`
147×	`distribute-rgt-in_binary64`
123×	`distribute-lft-in_binary64`
111×	`associate-l_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	24	967
1	54	967
2	126	839
3	294	839
4	892	647
5	1740	647
6	2771	647
7	3473	647
8	3596	647
9	3596	647

Stop Event

1×

saturated

Counts

158 → 100

prune72.0ms (2.2%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	100	0	100
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	100	7	107

Error

Counts

107 → 7

Alt Table

Status	Error	Program
✓	3.2b	(*.f64 (-.f64 (+.f64 (/.f64 y z) (/.f64 1 z)) 1) x)
✓	1.6b	(-.f64 (fma.f64 y (/.f64 x z) (/.f64 x z)) x)
✓	3.3b	(-.f64 (+.f64 (/.f64 (*.f64 y x) z) (/.f64 x z)) x)
	3.6b	(-.f64 (pow.f64 (/.f64 z (fma.f64 x y x)) -1) x)
	4.0b	(-.f64 (pow.f64 (cbrt.f64 (/.f64 (fma.f64 x y x) z)) 3) x)
	16.4b	(*.f64 (-.f64 (-.f64 (/.f64 (pow.f64 (/.f64 y z) 2) (/.f64 (-.f64 y 1) z)) (/.f64 (pow.f64 z -2) (/.f64 (-.f64 y 1) z))) 1) x)
	3.4b	(-.f64 (*.f64 (fma.f64 x y x) (/.f64 1 z)) x)

Compiler

Compiled 1747 to 850 computations (51.3% saved)

regimes330.0ms (10.2%)

Accuracy

Total 0.1b remaining (88.4%)

Threshold costs 0.1b (88.4%)

Counts

58 → 3

Compiler

Compiled 3404 to 2114 computations (37.9% saved)

bsearch27.0ms (0.8%)

Algorithm

2×	binary-search

Calls

2 calls:

13.0ms	x
12.0ms	x

Steps

Iters	Point		Range
4.719777420475578e-12	∈ [	4.11293720802786e-12	,	1.2046423543773445e-11	]
-839233400368095400.0	∈ [	-2.377765900218511e+20	,	-7649396889528970.0	]

Compiler

Compiled 4 to 3 computations (25% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	51
1	29	51
2	34	51
3	36	51
4	37	51

Stop Event

1×

saturated

end91.0ms (2.8%)

Stop Event

1×

fuel

Compiler

Compiled 185 to 113 computations (38.9% saved)

Details

analyze557.0ms (17.2%)

sample961.0ms (29.8%)

preprocess34.0ms (1.1%)

simplify28.0ms (0.9%)

prune3.0ms (0.1%)

localize6.0ms (0.2%)

series26.0ms (0.8%)

rewrite59.0ms (1.8%)

simplify72.0ms (2.2%)

prune98.0ms (3%)

localize7.0ms (0.2%)

series28.0ms (0.9%)

rewrite61.0ms (1.9%)

simplify58.0ms (1.8%)

prune106.0ms (3.3%)

localize8.0ms (0.2%)

series42.0ms (1.3%)

rewrite89.0ms (2.7%)

simplify56.0ms (1.7%)

prune254.0ms (7.9%)

localize5.0ms (0.2%)

series35.0ms (1.1%)

rewrite50.0ms (1.6%)

simplify63.0ms (1.9%)

prune72.0ms (2.2%)

regimes330.0ms (10.2%)

bsearch27.0ms (0.8%)

simplify4.0ms (0.1%)

end91.0ms (2.8%)

Profiling