Details

analyze142.0ms (7.5%)

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%	74.9%	0.1%	6
56.2%	43.7%	0.1%	7
56.2%	43.7%	0.1%	8
76.5%	23.4%	0.1%	9
76.5%	23.4%	0.1%	10
87.8%	12.1%	0.1%	11
87.8%	12.1%	0.1%	12
93.8%	6.1%	0.1%	13
93.8%	6.1%	0.1%	14

Compiler

Compiled 12 to 8 computations (33.3% saved)

sample803.0ms (42.4%)

Symmetry

(sort x y)

Results

763.0ms

8256×

body

128

valid

Compiler

Compiled 35 to 23 computations (34.3% saved)

simplify7.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

13×	`associate-/r*_binary64`
5×	`*-commutative_binary64`
4×	`associate-/l/_binary64`
3×	`associate-r_binary64`
3×	`associate-l_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	13
1	15	13
2	28	13
3	39	13
4	37	13
5	37	13

prune2.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

14.3b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	14.3b	(/.f64 (+.f64 x y) (.f64 (.f64 x 2) y))

Compiler

Compiled 42 to 25 computations (40.5% saved)

localize5.0ms (0.3%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	13.9b	(/.f64 (+.f64 x y) (.f64 (.f64 x 2) y))

series8.0ms (0.4%)

Counts

1 → 24

Calls

1 calls:

8.0ms

(/.f64 (+.f64 x y) (*.f64 (*.f64 x 2) y))

rewrite10.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-cbrt-cube_binary64`
10×	`add-exp-log_binary64`
7×	`*-un-lft-identity_binary64`
4×	`associate-/l*_binary64`
4×	`times-frac_binary64`

Counts

1 → 29

Calls

1 calls:

9.0ms

(/.f64 (+.f64 x y) (*.f64 (*.f64 x 2) y))

simplify53.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

701×	`fma-def_binary64`
664×	`times-frac_binary64`
522×	`associate-/r*_binary64`
519×	`associate-l_binary64`
500×	`distribute-rgt-in_binary64`

Counts

53 → 45

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	80	767
1	222	654
2	839	654
3	3818	653
4	5409	653

prune25.0ms (1.3%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	42	3	45
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	43	3	46

Error

Counts

46 → 3

Alt Table

Status	Error	Program
	14.2b	(*.f64 (+.f64 x y) (/.f64 (/.f64 1/2 x) y))
	7.9b	(*.f64 (/.f64 1/2 x) (/.f64 (+.f64 x y) y))
▶	0.0b	(+.f64 (/.f64 1/2 x) (/.f64 1/2 y))

Compiler

Compiled 752 to 370 computations (50.8% saved)

localize4.0ms (0.2%)

Local error

Found 1 expressions with local error:

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

series7.0ms (0.4%)

Counts

1 → 24

Calls

1 calls:

7.0ms

(+.f64 (/.f64 1/2 x) (/.f64 1/2 y))

rewrite11.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`*-un-lft-identity_binary64`
15×	`times-frac_binary64`
13×	`fma-def_binary64`
10×	`add-sqr-sqrt_binary64`
10×	`add-cube-cbrt_binary64`

Counts

1 → 32

Calls

1 calls:

9.0ms

(+.f64 (/.f64 1/2 x) (/.f64 1/2 y))

simplify86.0ms (4.6%)

Algorithm

1×	egg-herbie

Rules

539×	`distribute-rgt-out_binary64`
539×	`times-frac_binary64`
394×	`associate-/l/_binary64`
321×	`fma-neg_binary64`
298×	`distribute-rgt-in_binary64`

Counts

56 → 40

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	49	504
1	127	473
2	402	472
3	1379	472
4	2965	472
5	4451	472
6	4835	472
7	5030	472

prune23.0ms (1.2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	40	0	40
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	40	3	43

Error

Counts

43 → 3

Alt Table

Status	Error	Program
	14.2b	(*.f64 (+.f64 x y) (/.f64 (/.f64 1/2 x) y))
▶	7.9b	(*.f64 (/.f64 1/2 x) (/.f64 (+.f64 x y) y))
✓	0.0b	(+.f64 (/.f64 1/2 x) (/.f64 1/2 y))

Compiler

Compiled 588 to 430 computations (26.9% saved)

localize5.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (+.f64 x y) y)
✓	7.4b	(*.f64 (/.f64 1/2 x) (/.f64 (+.f64 x y) y))

series13.0ms (0.7%)

Counts

2 → 48

Calls

2 calls:

8.0ms	(*.f64 (/.f64 1/2 x) (/.f64 (+.f64 x y) y))
5.0ms	(/.f64 (+.f64 x y) y)

rewrite20.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

40×	`*-un-lft-identity_binary64`
38×	`add-sqr-sqrt_binary64`
37×	`times-frac_binary64`
26×	`add-cube-cbrt_binary64`
16×	`associate-r_binary64`

Counts

2 → 90

Calls

2 calls:

10.0ms	(*.f64 (/.f64 1/2 x) (/.f64 (+.f64 x y) y))
5.0ms	(/.f64 (+.f64 x y) y)

simplify86.0ms (4.5%)

Algorithm

1×	egg-herbie

Rules

924×	`distribute-rgt-in_binary64`
670×	`associate-*l/_binary64`
489×	`associate-/l*_binary64`
464×	`fma-def_binary64`
303×	`*-commutative_binary64`

Counts

138 → 123

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	143	1865
1	385	1697
2	1368	1651
3	3889	1651
4	5762	1651

prune58.0ms (3%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	123	0	123
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	123	3	126

Error

Counts

126 → 3

Alt Table

Status	Error	Program
▶	14.2b	(*.f64 (+.f64 x y) (/.f64 (/.f64 1/2 x) y))
✓	7.9b	(*.f64 (/.f64 1/2 x) (/.f64 (+.f64 x y) y))
✓	0.0b	(+.f64 (/.f64 1/2 x) (/.f64 1/2 y))

Compiler

Compiled 2032 to 868 computations (57.3% saved)

localize8.0ms (0.4%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 (/.f64 1/2 x) y)
✓	13.7b	(*.f64 (+.f64 x y) (/.f64 (/.f64 1/2 x) y))

series17.0ms (0.9%)

Counts

2 → 48

Calls

2 calls:

9.0ms	(/.f64 (/.f64 1/2 x) y)
8.0ms	(*.f64 (+.f64 x y) (/.f64 (/.f64 1/2 x) y))

rewrite33.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Rules

144×	`times-frac_binary64`
89×	`add-sqr-sqrt_binary64`
82×	`*-un-lft-identity_binary64`
80×	`add-cube-cbrt_binary64`
43×	`associate-r_binary64`

Counts

2 → 144

Calls

2 calls:

14.0ms	(*.f64 (+.f64 x y) (/.f64 (/.f64 1/2 x) y))
4.0ms	(/.f64 (/.f64 1/2 x) y)

simplify153.0ms (8.1%)

Algorithm

1×	egg-herbie

Rules

634×	`fma-def_binary64`
562×	`associate-/r*_binary64`
328×	`associate-/r/_binary64`
168×	`sub-neg_binary64`
159×	`associate-l_binary64`

Counts

192 → 215

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	237	3039
1	582	2868
2	2303	2868
3	3716	2868
4	4394	2867
5	4833	2867
6	5008	2867

prune180.0ms (9.5%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	215	0	215
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	215	3	218

Error

Counts

218 → 3

Alt Table

Status	Error	Program
✓	14.2b	(*.f64 (+.f64 x y) (/.f64 (/.f64 1/2 x) y))
✓	7.9b	(*.f64 (/.f64 1/2 x) (/.f64 (+.f64 x y) y))
✓	0.0b	(+.f64 (/.f64 1/2 x) (/.f64 1/2 y))

Compiler

Compiled 3910 to 1948 computations (50.2% saved)

regimes81.0ms (4.3%)

Accuracy

Total 0.0b remaining (53.8%)

Threshold costs 0.0b (53.8%)

Counts

11 → 1

Compiler

Compiled 370 to 256 computations (30.8% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	8	10
2	8	10

end51.0ms (2.7%)

Remove: (sort x y)
Compiler: Compiled 67 to 49 computations (26.9% saved)

Details

analyze142.0ms (7.5%)

sample803.0ms (42.4%)

simplify7.0ms (0.4%)

prune2.0ms (0.1%)

localize5.0ms (0.3%)

series8.0ms (0.4%)

rewrite10.0ms (0.5%)

simplify53.0ms (2.8%)

prune25.0ms (1.3%)

localize4.0ms (0.2%)

series7.0ms (0.4%)

rewrite11.0ms (0.6%)

simplify86.0ms (4.6%)

prune23.0ms (1.2%)

localize5.0ms (0.3%)

series13.0ms (0.7%)

rewrite20.0ms (1.1%)

simplify86.0ms (4.5%)

prune58.0ms (3%)

localize8.0ms (0.4%)

series17.0ms (0.9%)

rewrite33.0ms (1.7%)

simplify153.0ms (8.1%)

prune180.0ms (9.5%)

regimes81.0ms (4.3%)

simplify3.0ms (0.1%)

end51.0ms (2.7%)

Profiling