Details

analyze124.0ms (8.9%)

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)

sample117.0ms (8.4%)

Algorithm

1×

intervals

Results

8.0ms

256×

body

128

valid

Compiler

Compiled 25 to 17 computations (32% saved)

simplify61.0ms (4.4%)

Algorithm

1×	egg-herbie

Rules

959×	`fma-neg_binary64`
595×	`times-frac_binary64`
494×	`neg-mul-1_binary64`
491×	`neg-sub0_binary64`
301×	`associate-/l*_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	8	13
1	19	13
2	52	10
3	113	10
4	203	10
5	436	10
6	758	10
7	2592	10
8	4299	10
9	5002	10

prune4.0ms (0.3%)

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
▶	0.0b	(+.f64 (/.f64 1/2 y) (/.f64 -1/2 x))
	13.5b	(/.f64 (-.f64 x y) (.f64 (.f64 x 2) y))

Compiler

Compiled 58 to 40 computations (31% saved)

localize4.0ms (0.3%)

Local error

Found 1 expressions with local error:

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

series7.0ms (0.5%)

Counts

1 → 24

Calls

1 calls:

7.0ms

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

rewrite12.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`*-un-lft-identity_binary64`
13×	`fma-def_binary64`
11×	`times-frac_binary64`
8×	`add-sqr-sqrt_binary64`
8×	`add-cube-cbrt_binary64`

Counts

1 → 29

Calls

1 calls:

11.0ms

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

simplify87.0ms (6.2%)

Algorithm

1×	egg-herbie

Rules

889×	`div-sub_binary64`
786×	`sub-neg_binary64`
324×	`distribute-rgt-in_binary64`
310×	`associate-*l/_binary64`
292×	`distribute-lft-in_binary64`

Counts

53 → 44

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	41	466
1	128	436
2	336	435
3	1291	435
4	3780	435
5	4265	435
6	4960	435
7	5783	435

prune29.0ms (2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	42	2	44
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	42	4	46

Error

0.0b

Counts

46 → 4

Alt Table

Status	Error	Program
	29.8b	(/.f64 (-.f64 (.f64 (/.f64 1/2 y) (/.f64 1/2 y)) (.f64 (/.f64 -1/2 x) (/.f64 -1/2 x))) (-.f64 (/.f64 1/2 y) (/.f64 -1/2 x)))
	32.0b	(fma.f64 (sqrt.f64 (/.f64 1/2 y)) (sqrt.f64 (/.f64 1/2 y)) (/.f64 -1/2 x))
✓	0.0b	(+.f64 (/.f64 1/2 y) (/.f64 -1/2 x))
▶	13.5b	(/.f64 (-.f64 x y) (.f64 (.f64 x 2) y))

Compiler

Compiled 695 to 513 computations (26.2% saved)

localize5.0ms (0.3%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	13.1b	(/.f64 (-.f64 x y) (.f64 (.f64 x 2) y))

series8.0ms (0.6%)

Counts

1 → 24

Calls

1 calls:

8.0ms

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

rewrite10.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-cbrt-cube_binary64`
10×	`add-exp-log_binary64`
7×	`*-un-lft-identity_binary64`
7×	`add-sqr-sqrt_binary64`
5×	`associate-/l*_binary64`

Counts

1 → 32

Calls

1 calls:

6.0ms

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

simplify56.0ms (4%)

Algorithm

1×	egg-herbie

Rules

749×	`fma-def_binary64`
658×	`times-frac_binary64`
546×	`associate-/r*_binary64`
522×	`associate-l_binary64`
490×	`div-sub_binary64`

Counts

56 → 50

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	90	826
1	241	704
2	891	655
3	4160	655
4	6127	655

prune29.0ms (2.1%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	49	1	50
Fresh	1	1	2
Picked	1	0	1
Done	0	1	1
Total	51	3	54

Error

Counts

54 → 3

Alt Table

Status	Error	Program
	32.0b	(fma.f64 (sqrt.f64 (/.f64 1/2 y)) (sqrt.f64 (/.f64 1/2 y)) (/.f64 -1/2 x))
✓	0.0b	(+.f64 (/.f64 1/2 y) (/.f64 -1/2 x))
▶	6.6b	(/.f64 (/.f64 (-.f64 x y) (*.f64 x 2)) y)

Compiler

Compiled 803 to 418 computations (47.9% saved)

localize5.0ms (0.4%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 x y) (*.f64 x 2))
✓	6.2b	(/.f64 (/.f64 (-.f64 x y) (*.f64 x 2)) y)

series13.0ms (1%)

Counts

2 → 48

Calls

2 calls:

8.0ms	(/.f64 (/.f64 (-.f64 x y) (*.f64 x 2)) y)
6.0ms	(/.f64 (-.f64 x y) (*.f64 x 2))

rewrite18.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

52×	`times-frac_binary64`
34×	`*-un-lft-identity_binary64`
34×	`add-sqr-sqrt_binary64`
22×	`add-cube-cbrt_binary64`
16×	`add-cbrt-cube_binary64`

Counts

2 → 89

Calls

2 calls:

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

simplify83.0ms (5.9%)

Algorithm

1×	egg-herbie

Rules

838×	`div-sub_binary64`
625×	`times-frac_binary64`
503×	`associate-/l*_binary64`
486×	`associate-/l/_binary64`
485×	`associate-/r*_binary64`

Counts

137 → 124

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	162	2187
1	397	2004
2	1189	1907
3	4425	1899
4	6771	1899

prune49.0ms (3.5%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	123	1	124
Fresh	1	0	1
Picked	1	0	1
Done	0	1	1
Total	125	2	127

Error

Counts

127 → 2

Alt Table

Status	Error	Program
✓	0.0b	(+.f64 (/.f64 1/2 y) (/.f64 -1/2 x))
▶	6.6b	(/.f64 (fma.f64 -1/2 (/.f64 y x) 1/2) y)

Compiler

Compiled 1993 to 925 computations (53.6% saved)

localize5.0ms (0.3%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	6.2b	(/.f64 (fma.f64 -1/2 (/.f64 y x) 1/2) y)

series11.0ms (0.8%)

Counts

1 → 24

Calls

1 calls:

11.0ms

(/.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)

simplify65.0ms (4.6%)

Algorithm

1×	egg-herbie

Rules

498×	`distribute-rgt-out_binary64`
441×	`associate-l_binary64`
437×	`fma-def_binary64`
382×	`distribute-rgt-in_binary64`
376×	`distribute-lft-in_binary64`

Counts

53 → 55

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	62	781
1	113	735
2	249	735
3	539	733
4	1369	733
5	3308	733
6	4969	733

prune26.0ms (1.8%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	55	0	55
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	55	2	57

Error

Counts

57 → 2

Alt Table

Status	Error	Program
✓	0.0b	(+.f64 (/.f64 1/2 y) (/.f64 -1/2 x))
✓	6.6b	(/.f64 (fma.f64 -1/2 (/.f64 y x) 1/2) y)

Compiler

Compiled 906 to 544 computations (40% saved)

regimes60.0ms (4.3%)

Accuracy

Total 0.0b remaining (71.1%)

Threshold costs 0.0b (71.1%)

Counts

19 → 1

Compiler

Compiled 848 to 607 computations (28.4% saved)

simplify2.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	10
1	9	10
2	9	10

end0.0ms (0%)

Compiler: Compiled 9 to 7 computations (22.2% saved)

sample508.0ms (36.2%)

Algorithm

1×

intervals

Results

280.0ms	8000×	body	128	valid
0.0ms	2×	body	128	invalid

Compiler

Compiled 42 to 31 computations (26.2% saved)

Details

analyze124.0ms (8.9%)

sample117.0ms (8.4%)

simplify61.0ms (4.4%)

prune4.0ms (0.3%)

localize4.0ms (0.3%)

series7.0ms (0.5%)

rewrite12.0ms (0.9%)

simplify87.0ms (6.2%)

prune29.0ms (2%)

localize5.0ms (0.3%)

series8.0ms (0.6%)

rewrite10.0ms (0.7%)

simplify56.0ms (4%)

prune29.0ms (2.1%)

localize5.0ms (0.4%)

series13.0ms (1%)

rewrite18.0ms (1.3%)

simplify83.0ms (5.9%)

prune49.0ms (3.5%)

localize5.0ms (0.3%)

series11.0ms (0.8%)

rewrite3.0ms (0.2%)

simplify65.0ms (4.6%)

prune26.0ms (1.8%)

regimes60.0ms (4.3%)

simplify2.0ms (0.2%)

end0.0ms (0%)

sample508.0ms (36.2%)

Profiling