Details

analyze62.0ms (1.9%)

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
37.5%	62.4%	0.1%	5
43.7%	56.2%	0.1%	6
74.9%	25%	0.1%	7
81.2%	18.7%	0.1%	8
87.4%	12.5%	0.1%	9
90.5%	9.4%	0.1%	10
93.7%	6.2%	0.1%	11
95.2%	4.7%	0.1%	12
96.8%	3.1%	0.1%	13
97.6%	2.3%	0.1%	14

Compiler

Compiled 10 to 7 computations (30% saved)

sample1.2s (37.5%)

Results

1.1s	8255×	body	128	valid
0.0ms	1×	body	256	valid

Compiler

Compiled 29 to 20 computations (31% saved)

simplify53.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

546×	`fma-neg_binary64`
369×	`fma-def_binary64`
317×	`div-sub_binary64`
278×	`times-frac_binary64`
113×	`sub-neg_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	15	10
2	22	10
3	37	10
4	64	10
5	107	10
6	192	10
7	359	10
8	642	10
9	877	10
10	1142	10
11	1146	10
12	1156	10
13	1156	10
14	1064	10

prune2.0ms (0%)

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 → 1

Alt Table

Status	Error	Program
▶	0.0b	(/.f64 (-.f64 x y) (-.f64 1 y))

Compiler

Compiled 27 to 18 computations (33.3% saved)

localize4.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

series8.0ms (0.2%)

Counts

1 → 24

Calls

1 calls:

8.0ms

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

rewrite12.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

46×	`*-un-lft-identity_binary64`
46×	`add-sqr-sqrt_binary64`
30×	`times-frac_binary64`
19×	`difference-of-squares_binary64`
14×	`add-cube-cbrt_binary64`

Counts

1 → 60

Calls

1 calls:

8.0ms

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

simplify102.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

779×	`times-frac_binary64`
532×	`fma-neg_binary64`
266×	`fma-def_binary64`
231×	`div-sub_binary64`
213×	`associate--l+_binary64`

Counts

84 → 78

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	132	1541
1	341	1491
2	936	1482
3	2955	1482
4	4928	1482
5	5000	1482
6	4962	1482

prune57.0ms (1.7%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	75	3	78
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	76	3	79

Error

Counts

79 → 3

Alt Table

Status	Error	Program
	18.7b	(.f64 (/.f64 (-.f64 x y) (-.f64 1 (.f64 y y))) (+.f64 1 y))
▶	0.0b	(-.f64 (/.f64 x (-.f64 1 y)) (/.f64 y (-.f64 1 y)))
	16.4b	(/.f64 (/.f64 (-.f64 x y) (sqrt.f64 (-.f64 1 y))) (sqrt.f64 (-.f64 1 y)))

Compiler

Compiled 1333 to 673 computations (49.5% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

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

series12.0ms (0.4%)

Counts

2 → 24

Calls

2 calls:

10.0ms	(/.f64 x (-.f64 1 y))
2.0ms	(/.f64 y (-.f64 1 y))

rewrite13.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

48×	`*-un-lft-identity_binary64`
48×	`add-sqr-sqrt_binary64`
36×	`times-frac_binary64`
24×	`add-cube-cbrt_binary64`
16×	`difference-of-squares_binary64`

Counts

2 → 86

Calls

2 calls:

4.0ms	(/.f64 y (-.f64 1 y))
4.0ms	(/.f64 x (-.f64 1 y))

simplify84.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

559×	`fma-neg_binary64`
475×	`associate-/l/_binary64`
473×	`associate-/r*_binary64`
276×	`associate-/r/_binary64`
218×	`distribute-rgt-in_binary64`

Counts

110 → 122

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	159	1587
1	342	1503
2	899	1494
3	2106	1478
4	4585	1476
5	4920	1476

prune80.0ms (2.4%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	122	0	122
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	122	3	125

Error

Counts

125 → 3

Alt Table

Status	Error	Program
	18.7b	(.f64 (/.f64 (-.f64 x y) (-.f64 1 (.f64 y y))) (+.f64 1 y))
✓	0.0b	(-.f64 (/.f64 x (-.f64 1 y)) (/.f64 y (-.f64 1 y)))
▶	16.4b	(/.f64 (/.f64 (-.f64 x y) (sqrt.f64 (-.f64 1 y))) (sqrt.f64 (-.f64 1 y)))

Compiler

Compiled 2236 to 1411 computations (36.9% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (-.f64 1 y))
✓	0.0b	(/.f64 (/.f64 (-.f64 x y) (sqrt.f64 (-.f64 1 y))) (sqrt.f64 (-.f64 1 y)))
✓	0.1b	(/.f64 (-.f64 x y) (sqrt.f64 (-.f64 1 y)))

series39.0ms (1.2%)

Counts

3 → 44

Calls

3 calls:

22.0ms	(/.f64 (-.f64 x y) (sqrt.f64 (-.f64 1 y)))
9.0ms	(sqrt.f64 (-.f64 1 y))
8.0ms	(/.f64 (/.f64 (-.f64 x y) (sqrt.f64 (-.f64 1 y))) (sqrt.f64 (-.f64 1 y)))

rewrite158.0ms (4.8%)

Algorithm

1×	rewrite-expression-head

Rules

954×	`times-frac_binary64`
858×	`add-sqr-sqrt_binary64`
857×	`*-un-lft-identity_binary64`
654×	`sqrt-prod_binary64`
330×	`add-cube-cbrt_binary64`

Counts

3 → 637

Calls

3 calls:

23.0ms	(/.f64 (/.f64 (-.f64 x y) (sqrt.f64 (-.f64 1 y))) (sqrt.f64 (-.f64 1 y)))
7.0ms	(/.f64 (-.f64 x y) (sqrt.f64 (-.f64 1 y)))
3.0ms	(sqrt.f64 (-.f64 1 y))

simplify546.0ms (16.6%)

Algorithm

1×	egg-herbie

Rules

711×	`times-frac_binary64`
711×	`fma-def_binary64`
492×	`associate-/l/_binary64`
346×	`div-sub_binary64`
275×	`sub-neg_binary64`

Counts

681 → 548

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	485	24518
1	1130	23426
2	2728	22572
3	4986	22570
4	4988	22570

prune360.0ms (10.9%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	576	0	576
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	576	3	579

Error

Counts

579 → 3

Alt Table

Status	Error	Program
▶	18.7b	(.f64 (/.f64 (-.f64 x y) (-.f64 1 (.f64 y y))) (+.f64 1 y))
✓	0.0b	(-.f64 (/.f64 x (-.f64 1 y)) (/.f64 y (-.f64 1 y)))
✓	16.4b	(/.f64 (/.f64 (-.f64 x y) (sqrt.f64 (-.f64 1 y))) (sqrt.f64 (-.f64 1 y)))

Compiler

Compiled 16025 to 9793 computations (38.9% saved)

localize7.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (/.f64 (-.f64 x y) (-.f64 1 (.f64 y y))) (+.f64 1 y))
✓	17.9b	(/.f64 (-.f64 x y) (-.f64 1 (*.f64 y y)))

series57.0ms (1.7%)

Counts

2 → 48

Calls

2 calls:

32.0ms	(.f64 (/.f64 (-.f64 x y) (-.f64 1 (.f64 y y))) (+.f64 1 y))
25.0ms	(/.f64 (-.f64 x y) (-.f64 1 (*.f64 y y)))

rewrite29.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

64×	`add-sqr-sqrt_binary64`
61×	`*-un-lft-identity_binary64`
51×	`times-frac_binary64`
33×	`difference-of-squares_binary64`
31×	`associate-l_binary64`

Counts

2 → 113

Calls

2 calls:

11.0ms	(.f64 (/.f64 (-.f64 x y) (-.f64 1 (.f64 y y))) (+.f64 1 y))
10.0ms	(/.f64 (-.f64 x y) (-.f64 1 (*.f64 y y)))

simplify86.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

911×	`fma-def_binary64`
760×	`distribute-rgt-in_binary64`
393×	`times-frac_binary64`
163×	`cancel-sign-sub-inv_binary64`
155×	`sub-neg_binary64`

Counts

161 → 196

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	221	3816
1	736	3506
2	2218	3179
3	5251	3179

prune113.0ms (3.4%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	196	0	196
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	196	3	199

Error

Counts

199 → 3

Alt Table

Status	Error	Program
✓	18.7b	(.f64 (/.f64 (-.f64 x y) (-.f64 1 (.f64 y y))) (+.f64 1 y))
✓	0.0b	(-.f64 (/.f64 x (-.f64 1 y)) (/.f64 y (-.f64 1 y)))
✓	16.4b	(/.f64 (/.f64 (-.f64 x y) (sqrt.f64 (-.f64 1 y))) (sqrt.f64 (-.f64 1 y)))

Compiler

Compiled 4332 to 2191 computations (49.4% saved)

regimes116.0ms (3.5%)

Accuracy

Total 0.0b remaining (76.5%)

Threshold costs 0.0b (76.5%)

Counts

44 → 1

Compiler

Compiled 1619 to 1127 computations (30.4% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	16
1	14	16
2	22	16
3	26	16
4	28	16
5	27	16

end51.0ms (1.6%)

Compiler: Compiled 69 to 48 computations (30.4% saved)

Details

analyze62.0ms (1.9%)

sample1.2s (37.5%)

simplify53.0ms (1.6%)

prune2.0ms (0%)

localize4.0ms (0.1%)

series8.0ms (0.2%)

rewrite12.0ms (0.4%)

simplify102.0ms (3.1%)

prune57.0ms (1.7%)

localize5.0ms (0.2%)

series12.0ms (0.4%)

rewrite13.0ms (0.4%)

simplify84.0ms (2.5%)

prune80.0ms (2.4%)

localize6.0ms (0.2%)

series39.0ms (1.2%)

rewrite158.0ms (4.8%)

simplify546.0ms (16.6%)

prune360.0ms (10.9%)

localize7.0ms (0.2%)

series57.0ms (1.7%)

rewrite29.0ms (0.9%)

simplify86.0ms (2.6%)

prune113.0ms (3.4%)

regimes116.0ms (3.5%)

simplify2.0ms (0.1%)

end51.0ms (1.6%)

Profiling