Details

analyze100.0ms (5.6%)

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%	87.4%	12.6%	4
6.2%	74.9%	18.8%	5
12.5%	59.3%	28.2%	6
23.4%	43.7%	32.9%	7
28.1%	33.6%	38.3%	8
35.5%	23.4%	41.1%	9
38.2%	17.8%	44%	10
42.4%	12.1%	45.5%	11
43.9%	9.1%	47%	12
46.1%	6.1%	47.7%	13
46.9%	4.6%	48.5%	14

Compiler

Compiled 7 to 5 computations (28.6% saved)

sample709.0ms (39.3%)

Results

677.0ms	8256×	body	128	valid
20.0ms	247×	body	128	invalid

Compiler

Compiled 14 to 10 computations (28.6% saved)

preprocess17.0ms (0.9%)

Algorithm

2×	egg-herbie

Rules

1×	`swap-x-y`
1×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	12
1	7	12
0	2	2
1	2	2

Stop Event

1×	unsound
1×	saturated

Symmetry

(sort x y)

Compiler

Compiled 6 to 4 computations (33.3% saved)

simplify6.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	6
1	6	6

Stop Event

1×

saturated

Counts

1 → 1

prune1.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

0.0b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	0.0b	(sqrt.f64 (+.f64 x y))

Compiler

Compiled 18 to 12 computations (33.3% saved)

localize3.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (+.f64 x y))

series14.0ms (0.8%)

Counts

1 → 8

Calls

6 calls:

3.0ms	(sqrt.f64 (+.f64 x y))	x	0
3.0ms	(sqrt.f64 (+.f64 x y))	x	-inf
3.0ms	(sqrt.f64 (+.f64 x y))	y	-inf
2.0ms	(sqrt.f64 (+.f64 x y))	x	inf
2.0ms	(sqrt.f64 (+.f64 x y))	y	inf

rewrite36.0ms (2%)

Algorithm

1×	batch-egg-rewrite

Rules

553×	`log1p-expm1-u_binary64`
553×	`expm1-log1p-u_binary64`
455×	`prod-diff_binary64`
160×	`fma-def_binary64`
99×	`expm1-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	6
1	109	6
2	1479	6

Stop Event

1×	node limit

Counts

1 → 27

simplify30.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

846×	`fma-neg_binary64`
844×	`fma-def_binary64`
541×	`associate-l_binary64`
416×	`associate-r_binary64`
224×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	51	212
1	137	212
2	378	204
3	1199	198
4	4325	197

Stop Event

1×	node limit

Counts

35 → 41

prune27.0ms (1.5%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	39	2	41
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	39	3	42

Error

Counts

42 → 3

Alt Table

Status	Error	Program
✓	0.0b	(sqrt.f64 (+.f64 x y))
▶	0.5b	(pow.f64 (pow.f64 (+.f64 x y) 1/4) 2)
	15.6b	(fma.f64 x (fma.f64 1/2 (sqrt.f64 (/.f64 1 y)) (.f64 x (.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 3))) -1/8))) (fma.f64 1/16 (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 5))) (pow.f64 x 3)) (sqrt.f64 y)))

Compiler

Compiled 585 to 363 computations (37.9% saved)

localize6.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(pow.f64 (+.f64 x y) 1/4)
✓	0.5b	(pow.f64 (pow.f64 (+.f64 x y) 1/4) 2)

series44.0ms (2.4%)

Counts

2 → 48

Calls

12 calls:

12.0ms	(pow.f64 (pow.f64 (+.f64 x y) 1/4) 2)	y	-inf
4.0ms	(pow.f64 (pow.f64 (+.f64 x y) 1/4) 2)	x	-inf
3.0ms	(pow.f64 (pow.f64 (+.f64 x y) 1/4) 2)	x	0
3.0ms	(pow.f64 (pow.f64 (+.f64 x y) 1/4) 2)	x	inf
3.0ms	(pow.f64 (pow.f64 (+.f64 x y) 1/4) 2)	y	inf

rewrite42.0ms (2.4%)

Algorithm

1×	batch-egg-rewrite

Rules

751×	`log1p-expm1-u_binary64`
751×	`expm1-log1p-u_binary64`
455×	`prod-diff_binary64`
81×	`add-cbrt-cube_binary64`
80×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	14
1	181	13
2	2130	13

Stop Event

1×	node limit

Counts

2 → 46

simplify45.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

834×	`times-frac_binary64`
549×	`fma-def_binary64`
523×	`associate-/l*_binary64`
197×	`cancel-sign-sub-inv_binary64`
126×	`associate-/r/_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	162	1962
1	482	1934
2	1690	1608

Stop Event

1×	node limit

Counts

94 → 106

prune72.0ms (4%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	106	0	106
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	106	3	109

Error

Counts

109 → 3

Alt Table

Status	Error	Program
✓	0.0b	(sqrt.f64 (+.f64 x y))
✓	0.5b	(pow.f64 (pow.f64 (+.f64 x y) 1/4) 2)
▶	15.6b	(fma.f64 x (fma.f64 1/2 (sqrt.f64 (/.f64 1 y)) (.f64 x (.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 3))) -1/8))) (fma.f64 1/16 (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 5))) (pow.f64 x 3)) (sqrt.f64 y)))

Compiler

Compiled 2356 to 1668 computations (29.2% saved)

localize20.0ms (1.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	7.9b	(.f64 x (.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 3))) -1/8))
✓	12.6b	(sqrt.f64 (/.f64 1 (pow.f64 y 5)))
✓	15.4b	(*.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 5))) (pow.f64 x 3))
✓	19.0b	(sqrt.f64 (/.f64 1 (pow.f64 y 3)))

series90.0ms (5%)

Counts

4 → 12

Calls

18 calls:

14.0ms	(.f64 x (.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 3))) -1/8))	x	0
11.0ms	(.f64 x (.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 3))) -1/8))	x	-inf
11.0ms	(*.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 5))) (pow.f64 x 3))	x	inf
10.0ms	(*.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 5))) (pow.f64 x 3))	x	-inf
9.0ms	(*.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 5))) (pow.f64 x 3))	x	0

rewrite57.0ms (3.2%)

Algorithm

1×	batch-egg-rewrite

Rules

274×	`expm1-udef_binary64`
274×	`log1p-udef_binary64`
164×	`add-sqr-sqrt_binary64`
156×	`log1p-expm1-u_binary64`
156×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	17	36
1	363	28
2	4133	28

Stop Event

1×	node limit

Counts

4 → 91

simplify63.0ms (3.5%)

Algorithm

1×	egg-herbie

Rules

567×	`sqr-pow_binary64`
455×	`associate-/r*_binary64`
362×	`unswap-sqr_binary64`
322×	`associate-/l/_binary64`
256×	`cube-prod_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	180
1	25	180
2	43	180
3	59	180
4	94	180
5	230	180
6	792	180
7	2263	180
8	2351	180
9	2484	180
10	2642	180
11	2890	180
12	3218	180
13	3639	180
14	4139	180
15	4736	180

Stop Event

1×	node limit

Counts

103 → 93

prune125.0ms (7%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	93	0	93
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	93	3	96

Error

Counts

96 → 3

Alt Table

Status	Error	Program
✓	0.0b	(sqrt.f64 (+.f64 x y))
✓	0.5b	(pow.f64 (pow.f64 (+.f64 x y) 1/4) 2)
✓	15.6b	(fma.f64 x (fma.f64 1/2 (sqrt.f64 (/.f64 1 y)) (.f64 x (.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 3))) -1/8))) (fma.f64 1/16 (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 5))) (pow.f64 x 3)) (sqrt.f64 y)))

Compiler

Compiled 3050 to 2281 computations (25.2% saved)

regimes228.0ms (12.6%)

Accuracy

Total 0.0b remaining (51%)

Threshold costs 0.0b (51%)

Counts

41 → 1

Compiler

Compiled 4510 to 3494 computations (22.5% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	6
1	6	6

Stop Event

1×

saturated

end64.0ms (3.6%)

Stop Event

1×

done

Remove

(sort x y)

Compiler

Compiled 73 to 54 computations (26% saved)

Details

analyze100.0ms (5.6%)

sample709.0ms (39.3%)

preprocess17.0ms (0.9%)

simplify6.0ms (0.3%)

prune1.0ms (0.1%)

localize3.0ms (0.2%)

series14.0ms (0.8%)

rewrite36.0ms (2%)

simplify30.0ms (1.7%)

prune27.0ms (1.5%)

localize6.0ms (0.3%)

series44.0ms (2.4%)

rewrite42.0ms (2.4%)

simplify45.0ms (2.5%)

prune72.0ms (4%)

localize20.0ms (1.1%)

series90.0ms (5%)

rewrite57.0ms (3.2%)

simplify63.0ms (3.5%)

prune125.0ms (7%)

regimes228.0ms (12.6%)

simplify2.0ms (0.1%)

end64.0ms (3.6%)

Profiling