Details

analyze120.0ms (8.2%)

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
37.5%	50%	12.6%	6
43.7%	40.6%	15.7%	7
56.2%	23.4%	20.4%	8
57.8%	21.1%	21.2%	9
64%	12.5%	23.5%	10
64.8%	10.7%	24.5%	11
67.9%	6.4%	25.7%	12
68.3%	5.4%	26.3%	13
69.9%	3.3%	26.9%	14

Compiler

Compiled 12 to 8 computations (33.3% saved)

sample18.0ms (1.2%)

Algorithm

1×

intervals

Results

8.0ms	256×	body	128	valid
0.0ms	4×	body	128	invalid

Compiler

Compiled 25 to 17 computations (32% saved)

simplify25.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

71×	`distribute-rgt-in_binary64`
70×	`associate-l_binary64`
69×	`cancel-sign-sub-inv_binary64`
67×	`associate-r_binary64`
50×	`sub-neg_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	10
1	17	10
2	39	10
3	80	10
4	127	10
5	169	10
6	286	10
7	350	10
8	430	10
9	417	10
10	364	10

prune3.0ms (0.2%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

0.0b

Counts

2 → 2

Alt Table

Status	Error	Program
	0.0b	(.f64 2 (-.f64 (.f64 x x) (*.f64 x y)))
▶	0.0b	(.f64 2 (.f64 x (-.f64 x y)))

Compiler

Compiled 49 to 32 computations (34.7% saved)

localize4.0ms (0.3%)

Local error

Found 2 expressions with local error:

0.0b	(.f64 2 (.f64 x (-.f64 x y)))
0.0b	(*.f64 x (-.f64 x y))

rewrite46.0ms (3.2%)

Algorithm

1×	rewrite-expression-head

Error

Rules

20×	`distribute-lft-in_binary64`
20×	`distribute-rgt-in_binary64`
18×	`cancel-sign-sub-inv_binary64`
15×	`add-sqr-sqrt_binary64`
13×	`*-un-lft-identity_binary64`

Counts

2 → 66

Calls

2 calls:

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

Compiler

Compiled 866 to 346 computations (60% saved)

series37.0ms (2.5%)

Error

0.0b

Counts

2 → 24

Calls

2 calls:

18.0ms	(.f64 2 (.f64 x (-.f64 x y)))
16.0ms	(*.f64 x (-.f64 x y))

Compiler

Compiled 417 to 313 computations (24.9% saved)

simplify80.0ms (5.5%)

Algorithm

1×	egg-herbie

Rules

419×	`distribute-rgt-neg-out_binary64`
408×	`distribute-lft-neg-out_binary64`
347×	`exp-prod_binary64`
305×	`*-commutative_binary64`
293×	`unsub-neg_binary64`

Counts

90 → 75

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	113	1065
1	249	930
2	762	930
3	1911	930
4	4806	930
5	4980	930

prune18.0ms (1.2%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	73	2	75
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	74	3	77

Error

Counts

77 → 3

Alt Table

Status	Error	Program
	0.0b	(.f64 2 (-.f64 (.f64 x x) (*.f64 x y)))
▶	0.0b	(.f64 x (.f64 2 (-.f64 x y)))
	0.8b	(.f64 (sqrt.f64 2) (.f64 x (*.f64 (-.f64 x y) (sqrt.f64 2))))

Compiler

Compiled 361 to 194 computations (46.3% saved)

localize4.0ms (0.3%)

Local error

Found 1 expressions with local error:

0.0b	(.f64 x (.f64 2 (-.f64 x y)))

rewrite31.0ms (2.1%)

Algorithm

1×	rewrite-expression-head

Error

Rules

16×	`distribute-lft-in_binary64`
16×	`distribute-rgt-in_binary64`
12×	`cancel-sign-sub-inv_binary64`
6×	`*-un-lft-identity_binary64`
6×	`add-sqr-sqrt_binary64`

Counts

1 → 36

Calls

1 calls:

6.0ms

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

Compiler

Compiled 495 to 260 computations (47.5% saved)

series19.0ms (1.3%)

Error

Counts

1 → 12

Calls

1 calls:

18.0ms

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

Compiler

Compiled 221 to 169 computations (23.5% saved)

simplify63.0ms (4.3%)

Algorithm

1×	egg-herbie

Rules

827×	`neg-mul-1_binary64`
402×	`distribute-rgt-neg-out_binary64`
397×	`distribute-lft-neg-out_binary64`
283×	`*-commutative_binary64`
268×	`exp-prod_binary64`

Counts

48 → 36

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	97	646
1	215	565
2	619	565
3	1667	565
4	4235	565
5	5487	565

prune8.0ms (0.6%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	36	0	36
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	36	3	39

Error

Counts

39 → 3

Alt Table

Status	Error	Program
▶	0.0b	(.f64 2 (-.f64 (.f64 x x) (*.f64 x y)))
✓	0.0b	(.f64 x (.f64 2 (-.f64 x y)))
	0.8b	(.f64 (sqrt.f64 2) (.f64 x (*.f64 (-.f64 x y) (sqrt.f64 2))))

Compiler

Compiled 157 to 91 computations (42% saved)

localize5.0ms (0.4%)

Local error

Found 2 expressions with local error:

0.0b	(.f64 2 (-.f64 (.f64 x x) (*.f64 x y)))
0.0b	(-.f64 (.f64 x x) (.f64 x y))

rewrite25.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Error

Rules

6×	`add-sqr-sqrt_binary64`
4×	`associate-r_binary64`
4×	`*-un-lft-identity_binary64`
4×	`add-cube-cbrt_binary64`
4×	`add-cbrt-cube_binary64`

Counts

2 → 38

Calls

2 calls:

5.0ms	(.f64 2 (-.f64 (.f64 x x) (*.f64 x y)))
3.0ms	(-.f64 (.f64 x x) (.f64 x y))

Compiler

Compiled 625 to 194 computations (69% saved)

series38.0ms (2.6%)

Error

Counts

2 → 24

Calls

2 calls:

20.0ms	(.f64 2 (-.f64 (.f64 x x) (*.f64 x y)))
16.0ms	(-.f64 (.f64 x x) (.f64 x y))

Compiler

Compiled 417 to 313 computations (24.9% saved)

simplify72.0ms (4.9%)

Algorithm

1×	egg-herbie

Rules

497×	`associate-l_binary64`
428×	`associate-r_binary64`
273×	`times-frac_binary64`
177×	`distribute-lft-neg-out_binary64`
177×	`distribute-rgt-neg-out_binary64`

Counts

62 → 56

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	75	719
1	180	656
2	526	656
3	2153	656
4	4429	656
5	5100	656

prune14.0ms (0.9%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	56	0	56
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	56	3	59

Error

Counts

59 → 3

Alt Table

Status	Error	Program
✓	0.0b	(.f64 2 (-.f64 (.f64 x x) (*.f64 x y)))
✓	0.0b	(.f64 x (.f64 2 (-.f64 x y)))
▶	0.8b	(.f64 (sqrt.f64 2) (.f64 x (*.f64 (-.f64 x y) (sqrt.f64 2))))

Compiler

Compiled 454 to 211 computations (53.5% saved)

localize6.0ms (0.4%)

Local error

Found 3 expressions with local error:

0.2b	(.f64 x (.f64 (-.f64 x y) (sqrt.f64 2)))
0.4b	(.f64 (sqrt.f64 2) (.f64 x (*.f64 (-.f64 x y) (sqrt.f64 2))))
0.5b	(*.f64 (-.f64 x y) (sqrt.f64 2))

rewrite65.0ms (4.5%)

Algorithm

1×	rewrite-expression-head

Error

Rules

19×	`add-cbrt-cube_binary64`
19×	`add-exp-log_binary64`
19×	`pow1_binary64`
15×	`add-sqr-sqrt_binary64`
14×	`associate-l_binary64`

Counts

3 → 72

Calls

3 calls:

9.0ms	(.f64 (sqrt.f64 2) (.f64 x (*.f64 (-.f64 x y) (sqrt.f64 2))))
7.0ms	(*.f64 (-.f64 x y) (sqrt.f64 2))
6.0ms	(.f64 x (.f64 (-.f64 x y) (sqrt.f64 2)))

Compiler

Compiled 1154 to 731 computations (36.7% saved)

series84.0ms (5.8%)

Error

Counts

3 → 36

Calls

3 calls:

36.0ms	(.f64 (sqrt.f64 2) (.f64 x (*.f64 (-.f64 x y) (sqrt.f64 2))))
22.0ms	(.f64 x (.f64 (-.f64 x y) (sqrt.f64 2)))
20.0ms	(*.f64 (-.f64 x y) (sqrt.f64 2))

Compiler

Compiled 953 to 796 computations (16.5% saved)

simplify90.0ms (6.2%)

Algorithm

1×	egg-herbie

Rules

439×	`*-commutative_binary64`
304×	`distribute-rgt-in_binary64`
299×	`distribute-lft-in_binary64`
245×	`unswap-sqr_binary64`
213×	`associate-r_binary64`

Counts

108 → 89

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	108	1728
1	274	1409
2	905	1265
3	2316	1257
4	4787	1257
5	4996	1257

prune25.0ms (1.7%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	89	0	89
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	89	3	92

Error

Counts

92 → 3

Alt Table

Status	Error	Program
	0.0b	(.f64 2 (-.f64 (.f64 x x) (*.f64 x y)))
	0.0b	(.f64 x (.f64 2 (-.f64 x y)))
	0.8b	(.f64 (sqrt.f64 2) (.f64 x (*.f64 (-.f64 x y) (sqrt.f64 2))))

Compiler

Compiled 737 to 428 computations (41.9% saved)

regimes55.0ms (3.8%)

Accuracy

Total 0.0b remaining (92.8%)

Threshold costs 0.0b (92.8%)

Compiler

Compiled 616 to 400 computations (35.1% saved)

simplify3.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

3×	`*-commutative_binary64`
2×	`+-commutative_binary64`
2×	`sub-neg_binary64`
1×	`neg-sub0_binary64`
1×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	11	10
2	16	10
3	18	10
4	19	10
5	19	10

end0.0ms (0%)

Compiler: Compiled 9 to 6 computations (33.3% saved)

sample499.0ms (34.3%)

Algorithm

1×

intervals

Results

260.0ms	8000×	body	128	valid
5.0ms	177×	body	128	invalid

Compiler

Compiled 56 to 39 computations (30.4% saved)

Iter	Nodes	Cost
0	8	10
1	17	10
2	39	10
3	80	10
4	127	10
5	169	10
6	286	10
7	350	10
8	430	10
9	417	10
10	364	10

Iter	Nodes	Cost
0	8	10
1	17	10
2	39	10
3	80	10
4	127	10
5	169	10
6	286	10
7	350	10
8	430	10
9	417	10
10	364	10

Details

analyze120.0ms (8.2%)

sample18.0ms (1.2%)

simplify25.0ms (1.7%)

prune3.0ms (0.2%)

localize4.0ms (0.3%)

rewrite46.0ms (3.2%)

series37.0ms (2.5%)

simplify80.0ms (5.5%)

prune18.0ms (1.2%)

localize4.0ms (0.3%)

rewrite31.0ms (2.1%)

series19.0ms (1.3%)

simplify63.0ms (4.3%)

prune8.0ms (0.6%)

localize5.0ms (0.4%)

rewrite25.0ms (1.7%)

series38.0ms (2.6%)

simplify72.0ms (4.9%)

prune14.0ms (0.9%)

localize6.0ms (0.4%)

rewrite65.0ms (4.5%)

series84.0ms (5.8%)

simplify90.0ms (6.2%)

prune25.0ms (1.7%)

regimes55.0ms (3.8%)

simplify3.0ms (0.2%)

end0.0ms (0%)

sample499.0ms (34.3%)

Profiling

Iter	Nodes	Cost
0	8	10
1	17	10
2	39	10
3	80	10
4	127	10
5	169	10
6	286	10
7	350	10
8	430	10
9	417	10
10	364	10