Details

analyze127.0ms (7.8%)

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)

sample897.0ms (54.6%)

Symmetry

(sort x y)

Results

865.0ms

8256×

body

128

valid

Compiler

Compiled 35 to 23 computations (34.3% saved)

simplify14.0ms (0.8%)

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

18.7b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	18.7b	(/.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
✓	18.0b	(/.f64 (+.f64 x y) (.f64 (.f64 x 2) y))

series7.0ms (0.5%)

Counts

1 → 24

Calls

1 calls:

7.0ms

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

rewrite12.0ms (0.7%)

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:

5.0ms

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

simplify52.0ms (3.2%)

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

prune23.0ms (1.4%)

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
	8.1b	(/.f64 (/.f64 (+.f64 x y) (*.f64 x 2)) y)
	13.4b	(/.f64 (.f64 (cbrt.f64 (+.f64 x y)) (cbrt.f64 (+.f64 x y))) (/.f64 (.f64 x 2) (/.f64 (cbrt.f64 (+.f64 x y)) y)))
▶	0.0b	(+.f64 (/.f64 1/2 x) (/.f64 1/2 y))

Compiler

Compiled 774 to 376 computations (51.4% 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:

6.0ms

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

rewrite13.0ms (0.8%)

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:

11.0ms

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

simplify86.0ms (5.2%)

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

prune25.0ms (1.5%)

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
▶	8.1b	(/.f64 (/.f64 (+.f64 x y) (*.f64 x 2)) y)
	13.4b	(/.f64 (.f64 (cbrt.f64 (+.f64 x y)) (cbrt.f64 (+.f64 x y))) (/.f64 (.f64 x 2) (/.f64 (cbrt.f64 (+.f64 x y)) y)))
✓	0.0b	(+.f64 (/.f64 1/2 x) (/.f64 1/2 y))

Compiler

Compiled 610 to 436 computations (28.5% saved)

localize5.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (+.f64 x y) (*.f64 x 2))
✓	7.6b	(/.f64 (/.f64 (+.f64 x y) (*.f64 x 2)) y)

series18.0ms (1.1%)

Counts

2 → 48

Calls

2 calls:

11.0ms	(/.f64 (+.f64 x y) (*.f64 x 2))
8.0ms	(/.f64 (/.f64 (+.f64 x y) (*.f64 x 2)) y)

rewrite16.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

44×	`times-frac_binary64`
33×	`*-un-lft-identity_binary64`
21×	`add-sqr-sqrt_binary64`
21×	`add-cube-cbrt_binary64`
16×	`add-cbrt-cube_binary64`

Counts

2 → 81

Calls

2 calls:

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

simplify96.0ms (5.9%)

Algorithm

1×	egg-herbie

Rules

664×	`fma-def_binary64`
564×	`times-frac_binary64`
469×	`associate-/l*_binary64`
442×	`associate-/l/_binary64`
402×	`associate-/r*_binary64`

Counts

129 → 102

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	143	1982
1	348	1799
2	1033	1798
3	4078	1798
4	4673	1798
5	5550	1798

prune41.0ms (2.5%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	101	1	102
Fresh	1	0	1
Picked	1	0	1
Done	0	1	1
Total	103	2	105

Error

Counts

105 → 2

Alt Table

Status	Error	Program
✓	0.0b	(+.f64 (/.f64 1/2 x) (/.f64 1/2 y))
▶	8.1b	(/.f64 (fma.f64 1/2 (/.f64 y x) 1/2) y)

Compiler

Compiled 1655 to 763 computations (53.9% saved)

localize5.0ms (0.3%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	7.6b	(/.f64 (fma.f64 1/2 (/.f64 y x) 1/2) y)

series8.0ms (0.5%)

Counts

1 → 24

Calls

1 calls:

8.0ms

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

rewrite3.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`*-un-lft-identity_binary64`
9×	`times-frac_binary64`
9×	`add-sqr-sqrt_binary64`
9×	`add-cube-cbrt_binary64`
3×	`associate-/r*_binary64`

Counts

1 → 29

Calls

1 calls:

2.0ms

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

simplify76.0ms (4.6%)

Algorithm

1×	egg-herbie

Rules

980×	`fma-neg_binary64`
465×	`distribute-rgt-out_binary64`
441×	`associate-/r*_binary64`
418×	`fma-def_binary64`
378×	`distribute-rgt-in_binary64`

Counts

53 → 37

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	61	781
1	107	735
2	238	735
3	502	733
4	1397	733
5	3536	733
6	4560	733
7	5408	733

prune22.0ms (1.3%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	37	0	37
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	37	2	39

Error

Counts

39 → 2

Alt Table

Status	Error	Program
✓	0.0b	(+.f64 (/.f64 1/2 x) (/.f64 1/2 y))
✓	8.1b	(/.f64 (fma.f64 1/2 (/.f64 y x) 1/2) y)

Compiler

Compiled 592 to 344 computations (41.9% saved)

regimes32.0ms (1.9%)

Accuracy

Total 0.0b remaining (68%)

Threshold costs 0.0b (68%)

Counts

10 → 1

Compiler

Compiled 376 to 244 computations (35.1% 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

end46.0ms (2.8%)

Remove: (sort x y)
Compiler: Compiled 55 to 42 computations (23.6% saved)

Details

analyze127.0ms (7.8%)

sample897.0ms (54.6%)

simplify14.0ms (0.8%)

prune2.0ms (0.1%)

localize5.0ms (0.3%)

series7.0ms (0.5%)

rewrite12.0ms (0.7%)

simplify52.0ms (3.2%)

prune23.0ms (1.4%)

localize4.0ms (0.2%)

series7.0ms (0.4%)

rewrite13.0ms (0.8%)

simplify86.0ms (5.2%)

prune25.0ms (1.5%)

localize5.0ms (0.3%)

series18.0ms (1.1%)

rewrite16.0ms (1%)

simplify96.0ms (5.9%)

prune41.0ms (2.5%)

localize5.0ms (0.3%)

series8.0ms (0.5%)

rewrite3.0ms (0.2%)

simplify76.0ms (4.6%)

prune22.0ms (1.3%)

regimes32.0ms (1.9%)

simplify2.0ms (0.1%)

end46.0ms (2.8%)

Profiling