Details

analyze214.0ms (10.3%)

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)

sample868.0ms (42%)

Symmetry

(sort x y)

Results

832.0ms

8256×

body

128

valid

Compiler

Compiled 35 to 23 computations (34.3% saved)

simplify7.0ms (0.3%)

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

16.3b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	16.3b	(/.f64 (+.f64 x y) (.f64 (.f64 x 2) y))

Compiler

Compiled 42 to 25 computations (40.5% saved)

localize8.0ms (0.4%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	15.6b	(/.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))

rewrite7.0ms (0.4%)

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:

6.0ms

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

simplify54.0ms (2.6%)

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

prune26.0ms (1.2%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	43	2	45
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	44	2	46

Error

0.0b

Counts

46 → 2

Alt Table

Status	Error	Program
▶	0.0b	(+.f64 (/.f64 1/2 x) (/.f64 1/2 y))
	9.3b	(/.f64 1 (/.f64 (*.f64 x 2) (/.f64 (+.f64 x y) y)))

Compiler

Compiled 734 to 360 computations (51% 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))

series8.0ms (0.4%)

Counts

1 → 24

Calls

1 calls:

8.0ms

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

rewrite10.0ms (0.5%)

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))

simplify84.0ms (4.1%)

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

prune20.0ms (1%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	40	0	40
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	40	2	42

Error

0.0b

Counts

42 → 2

Alt Table

Status	Error	Program
✓	0.0b	(+.f64 (/.f64 1/2 x) (/.f64 1/2 y))
▶	9.3b	(/.f64 1 (/.f64 (*.f64 x 2) (/.f64 (+.f64 x y) y)))

Compiler

Compiled 570 to 420 computations (26.3% saved)

localize6.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 1 (/.f64 (*.f64 x 2) (/.f64 (+.f64 x y) y)))
✓	0.0b	(/.f64 (+.f64 x y) y)
✓	8.7b	(/.f64 (*.f64 x 2) (/.f64 (+.f64 x y) y))

series29.0ms (1.4%)

Counts

3 → 72

Calls

3 calls:

16.0ms	(/.f64 (*.f64 x 2) (/.f64 (+.f64 x y) y))
9.0ms	(/.f64 1 (/.f64 (*.f64 x 2) (/.f64 (+.f64 x y) y)))
4.0ms	(/.f64 (+.f64 x y) y)

rewrite44.0ms (2.1%)

Algorithm

1×	rewrite-expression-head

Rules

227×	`times-frac_binary64`
130×	`*-un-lft-identity_binary64`
86×	`add-sqr-sqrt_binary64`
86×	`add-cube-cbrt_binary64`
61×	`add-exp-log_binary64`

Counts

3 → 211

Calls

3 calls:

17.0ms	(/.f64 1 (/.f64 (*.f64 x 2) (/.f64 (+.f64 x y) y)))
6.0ms	(/.f64 (*.f64 x 2) (/.f64 (+.f64 x y) y))
3.0ms	(/.f64 (+.f64 x y) y)

simplify152.0ms (7.3%)

Algorithm

1×	egg-herbie

Rules

746×	`associate-/r*_binary64`
672×	`associate-l_binary64`
672×	`fma-def_binary64`
202×	`fma-neg_binary64`
166×	`associate-/r/_binary64`

Counts

283 → 289

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	238	5196
1	559	4711
2	1967	4498
3	4563	4486
4	5061	4486

prune134.0ms (6.5%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	288	1	289
Fresh	0	0	0
Picked	1	0	1
Done	0	1	1
Total	289	2	291

Error

Counts

291 → 2

Alt Table

Status	Error	Program
✓	0.0b	(+.f64 (/.f64 1/2 x) (/.f64 1/2 y))
▶	9.3b	(/.f64 1 (/.f64 (*.f64 x 2) (+.f64 (/.f64 x y) 1)))

Compiler

Compiled 5584 to 2478 computations (55.6% saved)

localize6.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (/.f64 x y) 1)
✓	0.0b	(/.f64 1 (/.f64 (*.f64 x 2) (+.f64 (/.f64 x y) 1)))
✓	8.7b	(/.f64 (*.f64 x 2) (+.f64 (/.f64 x y) 1))

series28.0ms (1.3%)

Counts

3 → 63

Calls

3 calls:

12.0ms	(/.f64 1 (/.f64 (*.f64 x 2) (+.f64 (/.f64 x y) 1)))
11.0ms	(/.f64 (*.f64 x 2) (+.f64 (/.f64 x y) 1))
4.0ms	(+.f64 (/.f64 x y) 1)

rewrite26.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

59×	`times-frac_binary64`
45×	`*-un-lft-identity_binary64`
31×	`add-sqr-sqrt_binary64`
31×	`add-cube-cbrt_binary64`
29×	`add-exp-log_binary64`

Counts

3 → 124

Calls

3 calls:

8.0ms	(/.f64 1 (/.f64 (*.f64 x 2) (+.f64 (/.f64 x y) 1)))
6.0ms	(/.f64 (*.f64 x 2) (+.f64 (/.f64 x y) 1))
5.0ms	(+.f64 (/.f64 x y) 1)

simplify95.0ms (4.6%)

Algorithm

1×	egg-herbie

Rules

750×	`fma-def_binary64`
639×	`associate-/l*_binary64`
444×	`associate-/r*_binary64`
346×	`associate-*l/_binary64`
323×	`associate-/r/_binary64`

Counts

187 → 194

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	156	3048
1	379	2686
2	1252	2510
3	4457	2492
4	5002	2492

prune103.0ms (5%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	194	0	194
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	194	2	196

Error

Counts

196 → 2

Alt Table

Status	Error	Program
✓	0.0b	(+.f64 (/.f64 1/2 x) (/.f64 1/2 y))
✓	9.3b	(/.f64 1 (/.f64 (*.f64 x 2) (+.f64 (/.f64 x y) 1)))

Compiler

Compiled 3656 to 2362 computations (35.4% saved)

regimes75.0ms (3.6%)

Accuracy

Total 0.0b remaining (61.1%)

Threshold costs 0.0b (61.1%)

Counts

25 → 1

Compiler

Compiled 853 to 610 computations (28.5% saved)

simplify2.0ms (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

end47.0ms (2.3%)

Remove: (sort x y)
Compiler: Compiled 58 to 45 computations (22.4% saved)

Details

analyze214.0ms (10.3%)

sample868.0ms (42%)

simplify7.0ms (0.3%)

prune2.0ms (0.1%)

localize8.0ms (0.4%)

series8.0ms (0.4%)

rewrite7.0ms (0.4%)

simplify54.0ms (2.6%)

prune26.0ms (1.2%)

localize4.0ms (0.2%)

series8.0ms (0.4%)

rewrite10.0ms (0.5%)

simplify84.0ms (4.1%)

prune20.0ms (1%)

localize6.0ms (0.3%)

series29.0ms (1.4%)

rewrite44.0ms (2.1%)

simplify152.0ms (7.3%)

prune134.0ms (6.5%)

localize6.0ms (0.3%)

series28.0ms (1.3%)

rewrite26.0ms (1.2%)

simplify95.0ms (4.6%)

prune103.0ms (5%)

regimes75.0ms (3.6%)

simplify2.0ms (0.1%)

end47.0ms (2.3%)

Profiling