Details

analyze92.0ms (3.5%)

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
25%	74.9%	0.1%	5
25%	50%	25.1%	6
25%	31.2%	43.8%	7
31.2%	25%	43.8%	8
39%	17.2%	43.8%	9
42.9%	13.3%	43.8%	10
47.2%	9%	43.8%	11
49.4%	6.8%	43.8%	12
51.6%	4.6%	43.8%	13
52.7%	3.5%	43.8%	14

Compiler

Compiled 18 to 8 computations (55.6% saved)

sample802.0ms (30.7%)

Results

771.0ms	8256×	body	128	valid
1.0ms	9×	body	128	invalid

Compiler

Compiled 53 to 23 computations (56.6% saved)

simplify7.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

28×	`fma-def_binary64`
4×	`*-commutative_binary64`
4×	`associate-+l+_binary64`
4×	`associate-r_binary64`
3×	`+-commutative_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	8	20
1	15	15
2	30	11
3	49	11
4	63	11
5	67	11
6	65	11

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

0.0b

Counts

3 → 2

Alt Table

Status	Error	Program
	0.1b	(fma.f64 y (.f64 y 3) (.f64 x x))
▶	0.1b	(+.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 y y)) (.f64 y y))

Compiler

Compiled 79 to 36 computations (54.4% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 y y))
✓	0.1b	(+.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 y y)) (.f64 y y))

series18.0ms (0.7%)

Counts

2 → 48

Calls

2 calls:

9.0ms	(+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 y y))
9.0ms	(+.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 y y)) (.f64 y y))

rewrite70.0ms (2.7%)

Algorithm

2×	batch-egg-rewrite

Rules

186× egg-rr

Counts

2 → 186

Calls

2 calls:

66.0ms	((+.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 y y)) (.f64 y y)) (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 y y)))
0.0ms	()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	34
1	190	23
2	2639	23
3	5021	23
0	0	0
1	0	0

simplify163.0ms (6.3%)

Algorithm

1×	egg-herbie

Rules

1078×	`sqr-pow_binary64`
786×	`cube-prod_binary64`
770×	`fabs-mul_binary64`
484×	`unswap-sqr_binary64`
392×	`pow-sqr_binary64`

Counts

234 → 195

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	462
1	25	462
2	44	462
3	82	462
4	177	462
5	445	462
6	653	462
7	1114	462
8	1161	462
9	1353	462
10	1558	462
11	1852	462
12	2136	462
13	2557	462
14	3190	462
15	3504	462
16	3856	462
17	4010	462
18	4078	462
19	4120	462
20	4917	462
21	4889	462

prune112.0ms (4.3%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	193	2	195
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	194	3	197

Error

Counts

197 → 3

Alt Table

Status	Error	Program
	0.1b	(fma.f64 y (.f64 y 3) (.f64 x x))
	0.3b	(pow.f64 (hypot.f64 y (hypot.f64 y (hypot.f64 x y))) 2)
▶	0.0b	(fma.f64 y (+.f64 y y) (pow.f64 (hypot.f64 x y) 2))

Compiler

Compiled 3607 to 1563 computations (56.7% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(hypot.f64 x y)
✓	0.0b	(pow.f64 (hypot.f64 x y) 2)
✓	0.0b	(fma.f64 y (+.f64 y y) (pow.f64 (hypot.f64 x y) 2))

series111.0ms (4.2%)

Counts

3 → 72

Calls

3 calls:

50.0ms	(pow.f64 (hypot.f64 x y) 2)
49.0ms	(fma.f64 y (+.f64 y y) (pow.f64 (hypot.f64 x y) 2))
11.0ms	(hypot.f64 x y)

rewrite47.0ms (1.8%)

Algorithm

2×	batch-egg-rewrite

Rules

66× egg-rr

Counts

3 → 66

Calls

2 calls:

45.0ms	((fma.f64 y (+.f64 y y) (pow.f64 (hypot.f64 x y) 2)) (pow.f64 (hypot.f64 x y) 2) (hypot.f64 x y))
0.0ms	()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	25
1	171	24
2	1752	24
3	5439	24
0	0	0
1	0	0

simplify61.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

755×	`fma-neg_binary64`
537×	`cancel-sign-sub-inv_binary64`
354×	`neg-mul-1_binary64`
312×	`distribute-rgt-neg-in_binary64`
310×	`distribute-lft-neg-in_binary64`

Counts

138 → 105

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	53	923
1	167	869
2	510	853
3	2182	853
4	4421	853
5	5037	853

prune57.0ms (2.2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	105	0	105
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	105	3	108

Error

Counts

108 → 3

Alt Table

Status	Error	Program
▶	0.1b	(fma.f64 y (.f64 y 3) (.f64 x x))
	0.3b	(pow.f64 (hypot.f64 y (hypot.f64 y (hypot.f64 x y))) 2)
✓	0.0b	(fma.f64 y (+.f64 y y) (pow.f64 (hypot.f64 x y) 2))

Compiler

Compiled 1747 to 828 computations (52.6% saved)

localize5.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 y (.f64 y 3) (.f64 x x))

series10.0ms (0.4%)

Counts

1 → 24

Calls

1 calls:

10.0ms

(fma.f64 y (*.f64 y 3) (*.f64 x x))

rewrite69.0ms (2.6%)

Algorithm

2×	batch-egg-rewrite

Rules

29× egg-rr

Counts

1 → 29

Calls

2 calls:

68.0ms	((fma.f64 y (.f64 y 3) (.f64 x x)))
0.0ms	()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	11
1	140	11
2	1507	11
3	4903	11
4	5114	11
0	0	0
1	0	0

simplify151.0ms (5.8%)

Algorithm

1×	egg-herbie

Rules

1238×	`sqr-pow_binary64`
688×	`fabs-mul_binary64`
666×	`cube-prod_binary64`
611×	`associate-l_binary64`
532×	`pow-sqr_binary64`

Counts

53 → 35

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	231
1	20	231
2	33	231
3	61	231
4	130	231
5	322	231
6	1004	231
7	1111	231
8	1273	231
9	1486	231
10	1757	231
11	2105	231
12	2536	231
13	2980	231
14	3730	231
15	4019	231
16	4362	231
17	4495	231
18	4546	231
19	4574	231
20	5448	231

prune19.0ms (0.7%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	35	0	35
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	35	3	38

Error

Counts

38 → 3

Alt Table

Status	Error	Program
✓	0.1b	(fma.f64 y (.f64 y 3) (.f64 x x))
▶	0.3b	(pow.f64 (hypot.f64 y (hypot.f64 y (hypot.f64 x y))) 2)
✓	0.0b	(fma.f64 y (+.f64 y y) (pow.f64 (hypot.f64 x y) 2))

Compiler

Compiled 498 to 284 computations (43% saved)

localize6.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(hypot.f64 x y)
✓	0.1b	(hypot.f64 y (hypot.f64 x y))
✓	0.1b	(hypot.f64 y (hypot.f64 y (hypot.f64 x y)))
✓	0.2b	(pow.f64 (hypot.f64 y (hypot.f64 y (hypot.f64 x y))) 2)

series302.0ms (11.6%)

Counts

3 → 72

Calls

3 calls:

235.0ms	(pow.f64 (hypot.f64 y (hypot.f64 y (hypot.f64 x y))) 2)
43.0ms	(hypot.f64 y (hypot.f64 y (hypot.f64 x y)))
24.0ms	(hypot.f64 y (hypot.f64 x y))

rewrite50.0ms (1.9%)

Algorithm

2×	batch-egg-rewrite

Rules

87× egg-rr

Counts

3 → 87

Calls

2 calls:

48.0ms	((pow.f64 (hypot.f64 y (hypot.f64 y (hypot.f64 x y))) 2) (hypot.f64 y (hypot.f64 y (hypot.f64 x y))) (hypot.f64 y (hypot.f64 x y)))
0.0ms	()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	30
1	164	30
2	1647	30
3	5297	30
0	0	0
1	0	0

simplify71.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

735×	`fma-neg_binary64`
698×	`times-frac_binary64`
451×	`fma-def_binary64`
316×	`associate-/l*_binary64`
311×	`associate-/r*_binary64`

Counts

159 → 161

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	127	1867
1	402	1530
2	1265	1471
3	4893	1471
4	5353	1471

prune132.0ms (5.1%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	212	0	212
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	212	3	215

Error

Counts

215 → 3

Alt Table

Status	Error	Program
✓	0.1b	(fma.f64 y (.f64 y 3) (.f64 x x))
✓	0.3b	(pow.f64 (hypot.f64 y (hypot.f64 y (hypot.f64 x y))) 2)
✓	0.0b	(fma.f64 y (+.f64 y y) (pow.f64 (hypot.f64 x y) 2))

Compiler

Compiled 4157 to 2420 computations (41.8% saved)

regimes189.0ms (7.3%)

Accuracy

Total 0.0b remaining (77.9%)

Threshold costs 0.0b (77.9%)

Counts

40 → 1

Compiler

Compiled 3175 to 1998 computations (37.1% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	14
1	8	14

end51.0ms (1.9%)

Compiler: Compiled 57 to 34 computations (40.4% saved)

Details

analyze92.0ms (3.5%)

sample802.0ms (30.7%)

simplify7.0ms (0.3%)

prune3.0ms (0.1%)

localize6.0ms (0.2%)

series18.0ms (0.7%)

rewrite70.0ms (2.7%)

simplify163.0ms (6.3%)

prune112.0ms (4.3%)

localize6.0ms (0.2%)

series111.0ms (4.2%)

rewrite47.0ms (1.8%)

simplify61.0ms (2.3%)

prune57.0ms (2.2%)

localize5.0ms (0.2%)

series10.0ms (0.4%)

rewrite69.0ms (2.6%)

simplify151.0ms (5.8%)

prune19.0ms (0.7%)

localize6.0ms (0.2%)

series302.0ms (11.6%)

rewrite50.0ms (1.9%)

simplify71.0ms (2.7%)

prune132.0ms (5.1%)

regimes189.0ms (7.3%)

simplify2.0ms (0.1%)

end51.0ms (1.9%)

Profiling