Details

analyze102.0ms (3.8%)

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
50%	50%	0.1%	4
50%	50%	0.1%	5
74.9%	25%	0.1%	6
74.9%	25%	0.1%	7
87.4%	12.5%	0.1%	8
87.4%	12.5%	0.1%	9
93.7%	6.2%	0.1%	10
93.7%	6.2%	0.1%	11
96.8%	3.1%	0.1%	12
96.8%	3.1%	0.1%	13
98.3%	1.6%	0.1%	14

Compiler

Compiled 10 to 7 computations (30% saved)

sample1.7s (64.5%)

Results

1.3s	7657×	body	128	valid
130.0ms	186×	body	2048	valid
105.0ms	204×	body	1024	valid
61.0ms	130×	body	512	valid
22.0ms	79×	body	256	valid
1.0ms	4×	body	128	invalid

Compiler

Compiled 29 to 20 computations (31% saved)

simplify35.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

254×	`fma-neg_binary64`
112×	`fma-def_binary64`
90×	`cancel-sign-sub-inv_binary64`
48×	`sub-neg_binary64`
40×	`distribute-rgt-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 7 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	13	10
2	24	10
3	43	10
4	79	10
5	146	10
6	244	10
7	348	8
8	442	8
9	595	8
10	650	8
11	590	8

prune5.0ms (0.2%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

0.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.1b	(fma.f64 (-.f64 x y) 1/2 x)

Compiler

Compiled 31 to 18 computations (41.9% saved)

localize8.0ms (0.3%)

Local error

Found 1 expressions with local error:

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

series8.0ms (0.3%)

Counts

1 → 24

Calls

1 calls:

8.0ms

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

rewrite73.0ms (2.7%)

Algorithm

2×	batch-egg-rewrite

Rules

666×	`log1p-expm1-u_binary64`
666×	`expm1-log1p-u_binary64`
408×	`prod-diff_binary64`
123×	`log1p-udef_binary64`
68×	`add-sqr-sqrt_binary64`

Counts

1 → 23

Calls

1 calls:

72.0ms

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	132	8
2	1638	8
3	5022	8
0	0	0
1	0	0

simplify54.0ms (2%)

Algorithm

1×	egg-herbie

Rules

120×	`fma-def_binary64`
71×	`fma-neg_binary64`
31×	`cancel-sign-sub-inv_binary64`
17×	`distribute-rgt-neg-in_binary64`
16×	`sub-neg_binary64`

Counts

47 → 27

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	204
1	18	168
2	26	168
3	40	168
4	61	168
5	87	168
6	137	168
7	177	168
8	215	168
9	234	168
10	250	168
11	254	168
12	212	168

prune44.0ms (1.6%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	21	6	27
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	22	6	28

Error

0.0b

Counts

28 → 6

Alt Table

Status	Error	Program
▶	0.1b	(fma.f64 -1/2 y (*.f64 3/2 x))
	28.1b	(pow.f64 (sqrt.f64 (fma.f64 (-.f64 x y) 1/2 x)) 2)
	1.3b	(pow.f64 (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x)) 3)
	35.2b	(/.f64 (-.f64 (.f64 (.f64 (-.f64 x y) 1/2) (.f64 (-.f64 x y) 1/2)) (.f64 x x)) (-.f64 (*.f64 (-.f64 x y) 1/2) x))
	45.6b	(/.f64 (+.f64 (pow.f64 (.f64 (-.f64 x y) 1/2) 3) (pow.f64 x 3)) (+.f64 (.f64 (.f64 (-.f64 x y) 1/2) (.f64 (-.f64 x y) 1/2)) (-.f64 (.f64 x x) (.f64 (*.f64 (-.f64 x y) 1/2) x))))
	1.4b	(*.f64 (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x)) (pow.f64 (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x)) 2))

Compiler

Compiled 505 to 293 computations (42% saved)

localize13.0ms (0.5%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 -1/2 y (*.f64 3/2 x))

series12.0ms (0.4%)

Counts

1 → 24

Calls

1 calls:

12.0ms

(fma.f64 -1/2 y (*.f64 3/2 x))

rewrite113.0ms (4.2%)

Algorithm

2×	batch-egg-rewrite

Rules

572×	`log1p-expm1-u_binary64`
572×	`expm1-log1p-u_binary64`
283×	`log-prod_binary64`
123×	`expm1-udef_binary64`
123×	`log1p-udef_binary64`

Counts

1 → 29

Calls

1 calls:

111.0ms

(fma.f64 -1/2 y (*.f64 3/2 x))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	8
1	141	8
2	1494	8
3	4931	8
4	4970	8
5	4883	8
0	0	0
1	0	0

simplify47.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

120×	`fma-def_binary64`
71×	`fma-neg_binary64`
31×	`cancel-sign-sub-inv_binary64`
17×	`distribute-rgt-neg-in_binary64`
16×	`sub-neg_binary64`

Counts

53 → 34

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	204
1	18	168
2	26	168
3	40	168
4	61	168
5	87	168
6	137	168
7	177	168
8	215	168
9	234	168
10	250	168
11	254	168
12	212	168

prune42.0ms (1.6%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	33	1	34
Fresh	5	0	5
Picked	1	0	1
Done	0	0	0
Total	39	1	40

Error

Counts

40 → 1

Alt Table

Status	Error	Program
▶	0b	(fma.f64 3/2 x (*.f64 y -1/2))

Compiler

Compiled 386 to 294 computations (23.8% saved)

localize8.0ms (0.3%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 3/2 x (*.f64 y -1/2))

series8.0ms (0.3%)

Counts

1 → 24

Calls

1 calls:

7.0ms

(fma.f64 3/2 x (*.f64 y -1/2))

rewrite120.0ms (4.4%)

Algorithm

2×	batch-egg-rewrite

Rules

572×	`log1p-expm1-u_binary64`
572×	`expm1-log1p-u_binary64`
283×	`log-prod_binary64`
123×	`expm1-udef_binary64`
123×	`log1p-udef_binary64`

Counts

1 → 29

Calls

1 calls:

118.0ms

(fma.f64 3/2 x (*.f64 y -1/2))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	8
1	141	8
2	1494	8
3	4931	8
4	4970	8
5	4883	8
0	0	0
1	0	0

simplify48.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

120×	`fma-def_binary64`
71×	`fma-neg_binary64`
31×	`cancel-sign-sub-inv_binary64`
17×	`distribute-rgt-neg-in_binary64`
16×	`sub-neg_binary64`

Counts

53 → 33

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	204
1	18	168
2	26	168
3	40	168
4	61	168
5	87	168
6	137	168
7	177	168
8	215	168
9	234	168
10	250	168
11	254	168
12	212	168

prune37.0ms (1.4%)

Pruning

1 alts after pruning (0 fresh and 1 done)

	Pruned	Kept	Total
New	33	0	33
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	33	1	34

Error

Counts

34 → 1

Alt Table

Status	Error	Program
✓	0b	(fma.f64 3/2 x (*.f64 y -1/2))

Compiler

Compiled 375 to 286 computations (23.7% saved)

regimes104.0ms (3.8%)

Accuracy

Total 0b remaining (0%)

Threshold costs 0b (0%)

Counts

15 → 1

Compiler

Compiled 594 to 392 computations (34% saved)

simplify4.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	8
1	8	8
2	8	8

end73.0ms (2.7%)

Compiler: Compiled 24 to 18 computations (25% saved)

Iter	Nodes	Cost
0	7	10
1	13	10
2	24	10
3	43	10
4	79	10
5	146	10
6	244	10
7	348	8
8	442	8
9	595	8
10	650	8
11	590	8

Iter	Nodes	Cost
0	10	204
1	18	168
2	26	168
3	40	168
4	61	168
5	87	168
6	137	168
7	177	168
8	215	168
9	234	168
10	250	168
11	254	168
12	212	168

Iter	Nodes	Cost
0	10	204
1	18	168
2	26	168
3	40	168
4	61	168
5	87	168
6	137	168
7	177	168
8	215	168
9	234	168
10	250	168
11	254	168
12	212	168

Iter	Nodes	Cost
0	10	204
1	18	168
2	26	168
3	40	168
4	61	168
5	87	168
6	137	168
7	177	168
8	215	168
9	234	168
10	250	168
11	254	168
12	212	168

Iter	Nodes	Cost
0	7	10
1	13	10
2	24	10
3	43	10
4	79	10
5	146	10
6	244	10
7	348	8
8	442	8
9	595	8
10	650	8
11	590	8

Iter	Nodes	Cost
0	10	204
1	18	168
2	26	168
3	40	168
4	61	168
5	87	168
6	137	168
7	177	168
8	215	168
9	234	168
10	250	168
11	254	168
12	212	168

Iter	Nodes	Cost
0	10	204
1	18	168
2	26	168
3	40	168
4	61	168
5	87	168
6	137	168
7	177	168
8	215	168
9	234	168
10	250	168
11	254	168
12	212	168

Iter	Nodes	Cost
0	10	204
1	18	168
2	26	168
3	40	168
4	61	168
5	87	168
6	137	168
7	177	168
8	215	168
9	234	168
10	250	168
11	254	168
12	212	168

Details

analyze102.0ms (3.8%)

sample1.7s (64.5%)

simplify35.0ms (1.3%)

prune5.0ms (0.2%)

localize8.0ms (0.3%)

series8.0ms (0.3%)

rewrite73.0ms (2.7%)

simplify54.0ms (2%)

prune44.0ms (1.6%)

localize13.0ms (0.5%)

series12.0ms (0.4%)

rewrite113.0ms (4.2%)

simplify47.0ms (1.8%)

prune42.0ms (1.6%)

localize8.0ms (0.3%)

series8.0ms (0.3%)

rewrite120.0ms (4.4%)

simplify48.0ms (1.8%)

prune37.0ms (1.4%)

regimes104.0ms (3.8%)

simplify4.0ms (0.2%)

end73.0ms (2.7%)

Profiling

Iter	Nodes	Cost
0	7	10
1	13	10
2	24	10
3	43	10
4	79	10
5	146	10
6	244	10
7	348	8
8	442	8
9	595	8
10	650	8
11	590	8

Iter	Nodes	Cost
0	10	204
1	18	168
2	26	168
3	40	168
4	61	168
5	87	168
6	137	168
7	177	168
8	215	168
9	234	168
10	250	168
11	254	168
12	212	168

Iter	Nodes	Cost
0	10	204
1	18	168
2	26	168
3	40	168
4	61	168
5	87	168
6	137	168
7	177	168
8	215	168
9	234	168
10	250	168
11	254	168
12	212	168

Iter	Nodes	Cost
0	10	204
1	18	168
2	26	168
3	40	168
4	61	168
5	87	168
6	137	168
7	177	168
8	215	168
9	234	168
10	250	168
11	254	168
12	212	168