Details

analyze16.0ms (0.6%)

Algorithm

1×

Search

True	Other	False	Iter
0%	18.7%	81.3%	0
0%	18.7%	81.3%	1
0%	18.7%	81.3%	2
0%	18.7%	81.3%	3
0%	18.7%	81.3%	4
4.7%	14%	81.3%	5
5.3%	13.5%	81.3%	6
18.1%	0.6%	81.3%	7
18.1%	0.6%	81.3%	8
18.6%	0.1%	81.3%	9
18.6%	0.1%	81.3%	10
18.7%	0%	81.3%	11
18.7%	0%	81.3%	12
18.7%	0%	81.3%	13
18.7%	0%	81.3%	14

Compiler

Compiled 28 to 17 computations (39.3% saved)

sample1.1s (38.1%)

Results

1.0s

8256×

body

128

valid

Compiler

Compiled 73 to 43 computations (41.1% saved)

simplify30.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

770×	`fma-def_binary64`
469×	`fma-neg_binary64`
365×	`sub-neg_binary64`
282×	`unsub-neg_binary64`
267×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	20
1	24	20
2	58	20
3	138	20
4	328	20
5	848	20
6	2017	20
7	4713	20

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

19.4b

Counts

3 → 2

Alt Table

Status	Error	Program
	20.0b	(.f64 (+.f64 x y) (/.f64 (-.f64 x y) (fma.f64 x x (.f64 y y))))
▶	19.8b	(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (*.f64 y y)))

Compiler

Compiled 97 to 46 computations (52.6% saved)

localize8.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (.f64 x x) (.f64 y y))
✓	19.5b	(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (*.f64 y y)))

series22.0ms (0.8%)

Counts

2 → 48

Calls

2 calls:

15.0ms	(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (*.f64 y y)))
7.0ms	(+.f64 (.f64 x x) (.f64 y y))

rewrite55.0ms (1.9%)

Algorithm

1×	batch-egg-rewrite

Rules

648×	`fma-def_binary64`
273×	`fma-neg_binary64`
211×	`expm1-udef_binary64`
211×	`log1p-udef_binary64`
121×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	28
1	237	26
2	3839	26

Stop Event

1×	node limit

Counts

2 → 93

Calls

2 calls:

53.0ms	(+.f64 (.f64 x x) (.f64 y y))
53.0ms	(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (*.f64 y y)))

simplify31.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

526×	`associate-*l/_binary64`
422×	`associate-*r/_binary64`
387×	`fma-def_binary64`
331×	`cancel-sign-sub-inv_binary64`
306×	`associate-/r/_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	37	738
1	111	678
2	333	642
3	1312	609

Stop Event

1×	node limit

Counts

141 → 112

prune72.0ms (2.5%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	108	4	112
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	110	4	114

Error

Counts

114 → 4

Alt Table

Status	Error	Program
	19.8b	(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (fma.f64 x x (.f64 y y)))
	43.2b	(fma.f64 (*.f64 (/.f64 y x) (/.f64 y x)) -2 1)
	19.7b	(fma.f64 2 (*.f64 (/.f64 x y) (-.f64 (/.f64 x y) (pow.f64 (/.f64 x y) 3))) -1)
▶	0.0b	(*.f64 (/.f64 (-.f64 x y) (hypot.f64 x y)) (/.f64 (+.f64 x y) (hypot.f64 x y)))

Compiler

Compiled 2234 to 891 computations (60.1% saved)

localize8.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

series47.0ms (1.7%)

Counts

4 → 96

Calls

4 calls:

20.0ms	(*.f64 (/.f64 (-.f64 x y) (hypot.f64 x y)) (/.f64 (+.f64 x y) (hypot.f64 x y)))
10.0ms	(hypot.f64 x y)
9.0ms	(/.f64 (+.f64 x y) (hypot.f64 x y))
8.0ms	(/.f64 (-.f64 x y) (hypot.f64 x y))

rewrite110.0ms (3.9%)

Algorithm

1×	batch-egg-rewrite

Rules

805×	`prod-diff_binary64`
279×	`egg-rr`
112×	`add-sqr-sqrt_binary64`
106×	`log1p-expm1-u_binary64`
106×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	46
1	214	43
2	3520	43

Stop Event

1×	node limit

Counts

4 → 279

Calls

4 calls:

101.0ms	(hypot.f64 x y)
101.0ms	(/.f64 (-.f64 x y) (hypot.f64 x y))
101.0ms	(/.f64 (+.f64 x y) (hypot.f64 x y))
101.0ms	(*.f64 (/.f64 (-.f64 x y) (hypot.f64 x y)) (/.f64 (+.f64 x y) (hypot.f64 x y)))

simplify56.0ms (2%)

Algorithm

1×	egg-herbie

Rules

553×	`times-frac_binary64`
372×	`fma-def_binary64`
296×	`associate-/l*_binary64`
286×	`cancel-sign-sub-inv_binary64`
270×	`associate-/r*_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	111	1812
1	388	1722
2	1344	1606

Stop Event

1×	node limit

Counts

375 → 369

prune301.0ms (10.7%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	417	1	418
Fresh	1	2	3
Picked	0	1	1
Done	0	0	0
Total	418	4	422

Error

Counts

422 → 4

Alt Table

Status	Error	Program
	43.2b	(fma.f64 (*.f64 (/.f64 y x) (/.f64 y x)) -2 1)
	19.7b	(fma.f64 2 (*.f64 (/.f64 x y) (-.f64 (/.f64 x y) (pow.f64 (/.f64 x y) 3))) -1)
✓	0.0b	(*.f64 (/.f64 (-.f64 x y) (hypot.f64 x y)) (/.f64 (+.f64 x y) (hypot.f64 x y)))
▶	0.0b	(/.f64 (+.f64 x y) (*.f64 (/.f64 (hypot.f64 x y) (-.f64 x y)) (hypot.f64 x y)))

Compiler

Compiled 15084 to 3907 computations (74.1% saved)

localize8.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

series49.0ms (1.7%)

Counts

3 → 72

Calls

3 calls:

30.0ms	(/.f64 (+.f64 x y) (*.f64 (/.f64 (hypot.f64 x y) (-.f64 x y)) (hypot.f64 x y)))
11.0ms	(/.f64 (hypot.f64 x y) (-.f64 x y))
8.0ms	(*.f64 (/.f64 (hypot.f64 x y) (-.f64 x y)) (hypot.f64 x y))

rewrite58.0ms (2.1%)

Algorithm

1×	batch-egg-rewrite

Rules

650×	`prod-diff_binary64`
200×	`log1p-udef_binary64`
110×	`add-sqr-sqrt_binary64`
104×	`log1p-expm1-u_binary64`
104×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	48
1	210	42
2	3295	42

Stop Event

1×	node limit

Counts

3 → 100

Calls

3 calls:

55.0ms	(/.f64 (+.f64 x y) (*.f64 (/.f64 (hypot.f64 x y) (-.f64 x y)) (hypot.f64 x y)))
55.0ms	(*.f64 (/.f64 (hypot.f64 x y) (-.f64 x y)) (hypot.f64 x y))
55.0ms	(/.f64 (hypot.f64 x y) (-.f64 x y))

simplify48.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

921×	`fma-neg_binary64`
434×	`times-frac_binary64`
258×	`fma-def_binary64`
223×	`associate-/l*_binary64`
203×	`associate-/r*_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	87	1233
1	276	1185
2	931	1102
3	4368	1089

Stop Event

1×	node limit

Counts

172 → 152

prune156.0ms (5.5%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	249	1	250
Fresh	1	1	2
Picked	0	1	1
Done	0	1	1
Total	250	4	254

Error

Counts

254 → 4

Alt Table

Status	Error	Program
▶	9.8b	(/.f64 (+.f64 x y) (pow.f64 (/.f64 (hypot.f64 x y) (sqrt.f64 (-.f64 x y))) 2))
	19.7b	(fma.f64 2 (*.f64 (/.f64 x y) (-.f64 (/.f64 x y) (pow.f64 (/.f64 x y) 3))) -1)
✓	0.0b	(*.f64 (/.f64 (-.f64 x y) (hypot.f64 x y)) (/.f64 (+.f64 x y) (hypot.f64 x y)))
✓	0.0b	(/.f64 (+.f64 x y) (*.f64 (/.f64 (hypot.f64 x y) (-.f64 x y)) (hypot.f64 x y)))

Compiler

Compiled 5342 to 2075 computations (61.2% saved)

localize9.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(hypot.f64 x y)
✓	0.0b	(/.f64 (+.f64 x y) (pow.f64 (/.f64 (hypot.f64 x y) (sqrt.f64 (-.f64 x y))) 2))
✓	0.4b	(/.f64 (hypot.f64 x y) (sqrt.f64 (-.f64 x y)))
✓	0.4b	(pow.f64 (/.f64 (hypot.f64 x y) (sqrt.f64 (-.f64 x y))) 2)

series106.0ms (3.8%)

Counts

3 → 36

Calls

3 calls:

48.0ms	(pow.f64 (/.f64 (hypot.f64 x y) (sqrt.f64 (-.f64 x y))) 2)
30.0ms	(/.f64 (hypot.f64 x y) (sqrt.f64 (-.f64 x y)))
28.0ms	(/.f64 (+.f64 x y) (pow.f64 (/.f64 (hypot.f64 x y) (sqrt.f64 (-.f64 x y))) 2))

rewrite60.0ms (2.1%)

Algorithm

1×	batch-egg-rewrite

Rules

659×	`prod-diff_binary64`
220×	`log1p-udef_binary64`
124×	`add-sqr-sqrt_binary64`
120×	`log1p-expm1-u_binary64`
120×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	48
1	250	44
2	3479	44

Stop Event

1×	node limit

Counts

3 → 105

Calls

3 calls:

58.0ms	(/.f64 (+.f64 x y) (pow.f64 (/.f64 (hypot.f64 x y) (sqrt.f64 (-.f64 x y))) 2))
58.0ms	(/.f64 (hypot.f64 x y) (sqrt.f64 (-.f64 x y)))
58.0ms	(pow.f64 (/.f64 (hypot.f64 x y) (sqrt.f64 (-.f64 x y))) 2)

simplify33.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

528×	`associate-/l*_binary64`
464×	`fma-def_binary64`
461×	`associate-/r*_binary64`
329×	`associate-l_binary64`
184×	`associate-*l/_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	123	1003
1	374	945
2	1395	896

Stop Event

1×	node limit

Counts

141 → 147

prune115.0ms (4.1%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	196	0	196
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	196	4	200

Error

Counts

200 → 4

Alt Table

Status	Error	Program
✓	9.8b	(/.f64 (+.f64 x y) (pow.f64 (/.f64 (hypot.f64 x y) (sqrt.f64 (-.f64 x y))) 2))
	19.7b	(fma.f64 2 (*.f64 (/.f64 x y) (-.f64 (/.f64 x y) (pow.f64 (/.f64 x y) 3))) -1)
✓	0.0b	(*.f64 (/.f64 (-.f64 x y) (hypot.f64 x y)) (/.f64 (+.f64 x y) (hypot.f64 x y)))
✓	0.0b	(/.f64 (+.f64 x y) (*.f64 (/.f64 (hypot.f64 x y) (-.f64 x y)) (hypot.f64 x y)))

Compiler

Compiled 4397 to 1942 computations (55.8% saved)

regimes281.0ms (10%)

Accuracy

Total 0.0b remaining (61.8%)

Threshold costs 0.0b (61.8%)

Counts

104 → 1

Compiler

Compiled 4831 to 2963 computations (38.7% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	22
1	12	22
2	17	22
3	19	22
4	20	22

Stop Event

1×

saturated

end64.0ms (2.3%)

Compiler: Compiled 102 to 52 computations (49% saved)

Details

analyze16.0ms (0.6%)

sample1.1s (38.1%)

simplify30.0ms (1.1%)

prune3.0ms (0.1%)

localize8.0ms (0.3%)

series22.0ms (0.8%)

rewrite55.0ms (1.9%)

simplify31.0ms (1.1%)

prune72.0ms (2.5%)

localize8.0ms (0.3%)

series47.0ms (1.7%)

rewrite110.0ms (3.9%)

simplify56.0ms (2%)

prune301.0ms (10.7%)

localize8.0ms (0.3%)

series49.0ms (1.7%)

rewrite58.0ms (2.1%)

simplify48.0ms (1.7%)

prune156.0ms (5.5%)

localize9.0ms (0.3%)

series106.0ms (3.8%)

rewrite60.0ms (2.1%)

simplify33.0ms (1.2%)

prune115.0ms (4.1%)

regimes281.0ms (10%)

simplify2.0ms (0.1%)

end64.0ms (2.3%)

Profiling