Details

analyze465.0ms (16.7%)

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)

sample32.0ms (1.2%)

Algorithm

1×

intervals

Results

19.0ms

256×

body

128

valid

Compiler

Compiled 25 to 17 computations (32% saved)

simplify72.0ms (2.6%)

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

prune7.0ms (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
	15.8b	(/.f64 (-.f64 x y) (.f64 (.f64 x 2) y))
▶	0.0b	(+.f64 (/.f64 1/2 y) (/.f64 -1/2 x))

Compiler

Compiled 58 to 40 computations (31% saved)

localize9.0ms (0.3%)

Local error

Found 1 expressions with local error:

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

series19.0ms (0.7%)

Counts

1 → 24

Calls

1 calls:

19.0ms

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

rewrite28.0ms (1%)

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:

25.0ms

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

simplify112.0ms (4%)

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

prune51.0ms (1.8%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	43	1	44
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	43	3	46

Error

0.0b

Counts

46 → 3

Alt Table

Status	Error	Program
	15.8b	(/.f64 (-.f64 x y) (.f64 (.f64 x 2) y))
▶	0.4b	(fma.f64 (/.f64 (sqrt.f64 1/2) 1) (/.f64 (sqrt.f64 1/2) y) (/.f64 -1/2 x))
✓	0.0b	(+.f64 (/.f64 1/2 y) (/.f64 -1/2 x))

Compiler

Compiled 645 to 477 computations (26% saved)

localize16.0ms (0.6%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.2b	(fma.f64 (/.f64 (sqrt.f64 1/2) 1) (/.f64 (sqrt.f64 1/2) y) (/.f64 -1/2 x))
✓	0.5b	(/.f64 (sqrt.f64 1/2) y)

series37.0ms (1.3%)

Counts

2 → 24

Calls

2 calls:

30.0ms	(fma.f64 (/.f64 (sqrt.f64 1/2) 1) (/.f64 (sqrt.f64 1/2) y) (/.f64 -1/2 x))
7.0ms	(/.f64 (sqrt.f64 1/2) y)

rewrite12.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`times-frac_binary64`
17×	`*-un-lft-identity_binary64`
17×	`add-sqr-sqrt_binary64`
17×	`add-cube-cbrt_binary64`
12×	`sqrt-prod_binary64`

Counts

2 → 51

Calls

2 calls:

6.0ms	(/.f64 (sqrt.f64 1/2) y)
1.0ms	(fma.f64 (/.f64 (sqrt.f64 1/2) 1) (/.f64 (sqrt.f64 1/2) y) (/.f64 -1/2 x))

simplify108.0ms (3.9%)

Algorithm

1×	egg-herbie

Rules

686×	`distribute-rgt-in_binary64`
649×	`distribute-lft-in_binary64`
199×	`times-frac_binary64`
195×	`associate-l_binary64`
194×	`associate-/l*_binary64`

Counts

75 → 66

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	85	883
1	137	850
2	252	850
3	594	850
4	2111	850
5	5226	850

prune81.0ms (2.9%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	66	0	66
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	66	3	69

Error

0.0b

Counts

69 → 3

Alt Table

Status	Error	Program
▶	15.8b	(/.f64 (-.f64 x y) (.f64 (.f64 x 2) y))
✓	0.4b	(fma.f64 (/.f64 (sqrt.f64 1/2) 1) (/.f64 (sqrt.f64 1/2) y) (/.f64 -1/2 x))
✓	0.0b	(+.f64 (/.f64 1/2 y) (/.f64 -1/2 x))

Compiler

Compiled 1184 to 960 computations (18.9% saved)

localize11.0ms (0.4%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	15.2b	(/.f64 (-.f64 x y) (.f64 (.f64 x 2) y))

series17.0ms (0.6%)

Counts

1 → 24

Calls

1 calls:

17.0ms

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

rewrite19.0ms (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:

15.0ms

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

simplify87.0ms (3.1%)

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

prune49.0ms (1.8%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	48	2	50
Fresh	0	0	0
Picked	1	0	1
Done	1	1	2
Total	50	3	53

Error

Counts

53 → 3

Alt Table

Status	Error	Program
	6.6b	(/.f64 1 (/.f64 (*.f64 x 2) (/.f64 (-.f64 x y) y)))
▶	6.4b	(*.f64 (/.f64 1/2 x) (/.f64 (-.f64 x y) y))
✓	0.0b	(+.f64 (/.f64 1/2 y) (/.f64 -1/2 x))

Compiler

Compiled 801 to 414 computations (48.3% saved)

localize11.0ms (0.4%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 x y) y)
✓	6.0b	(*.f64 (/.f64 1/2 x) (/.f64 (-.f64 x y) y))

series29.0ms (1%)

Counts

2 → 48

Calls

2 calls:

18.0ms	(*.f64 (/.f64 1/2 x) (/.f64 (-.f64 x y) y))
10.0ms	(/.f64 (-.f64 x y) y)

rewrite55.0ms (2%)

Algorithm

1×	rewrite-expression-head

Rules

54×	`add-sqr-sqrt_binary64`
43×	`times-frac_binary64`
42×	`*-un-lft-identity_binary64`
28×	`add-cube-cbrt_binary64`
19×	`associate-r_binary64`

Counts

2 → 98

Calls

2 calls:

27.0ms	(*.f64 (/.f64 1/2 x) (/.f64 (-.f64 x y) y))
12.0ms	(/.f64 (-.f64 x y) y)

simplify151.0ms (5.4%)

Algorithm

1×	egg-herbie

Rules

749×	`fma-def_binary64`
533×	`associate-/l*_binary64`
360×	`distribute-rgt-in_binary64`
337×	`distribute-lft-in_binary64`
281×	`associate-/l/_binary64`

Counts

146 → 147

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	158	2014
1	412	1844
2	1577	1795
3	4715	1795
4	5290	1795

prune126.0ms (4.5%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	147	0	147
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	147	3	150

Error

Counts

150 → 3

Alt Table

Status	Error	Program
	6.6b	(/.f64 1 (/.f64 (*.f64 x 2) (/.f64 (-.f64 x y) y)))
✓	6.4b	(*.f64 (/.f64 1/2 x) (/.f64 (-.f64 x y) y))
✓	0.0b	(+.f64 (/.f64 1/2 y) (/.f64 -1/2 x))

Compiler

Compiled 2461 to 1041 computations (57.7% saved)

regimes99.0ms (3.6%)

Accuracy

Total 0.0b remaining (66.2%)

Threshold costs 0.0b (66.2%)

Counts

17 → 1

Compiler

Compiled 571 to 412 computations (27.8% saved)

simplify4.0ms (0.1%)

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

end1.0ms (0%)

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

sample1.1s (38.5%)

Algorithm

1×

intervals

Results

592.0ms

8000×

body

128

valid

Compiler

Compiled 56 to 40 computations (28.6% saved)

Details

analyze465.0ms (16.7%)

sample32.0ms (1.2%)

simplify72.0ms (2.6%)

prune7.0ms (0.3%)

localize9.0ms (0.3%)

series19.0ms (0.7%)

rewrite28.0ms (1%)

simplify112.0ms (4%)

prune51.0ms (1.8%)

localize16.0ms (0.6%)

series37.0ms (1.3%)

rewrite12.0ms (0.4%)

simplify108.0ms (3.9%)

prune81.0ms (2.9%)

localize11.0ms (0.4%)

series17.0ms (0.6%)

rewrite19.0ms (0.7%)

simplify87.0ms (3.1%)

prune49.0ms (1.8%)

localize11.0ms (0.4%)

series29.0ms (1%)

rewrite55.0ms (2%)

simplify151.0ms (5.4%)

prune126.0ms (4.5%)

regimes99.0ms (3.6%)

simplify4.0ms (0.1%)

end1.0ms (0%)

sample1.1s (38.5%)

Profiling