Details

analyze49.0ms (4%)

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)

sample894.0ms (72.9%)

Results

695.0ms	7640×	body	128	valid
65.0ms	180×	body	2048	valid
56.0ms	205×	body	1024	valid
28.0ms	149×	body	512	valid
11.0ms	82×	body	256	valid

Compiler

Compiled 20 to 14 computations (30% saved)

preprocess34.0ms (2.8%)

Algorithm

2×	egg-herbie

Rules

446×	`fma-neg_binary64`
114×	`fma-def_binary64`
90×	`cancel-sign-sub-inv_binary64`
62×	`sub-neg_binary64`
52×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	20
1	20	20
2	40	20
3	74	20
4	155	20
5	322	20
6	623	16
7	990	16
8	1288	16
9	1348	16
10	1352	16
0	2	2

Stop Event

1×	saturated
1×	saturated

Compiler

Compiled 9 to 6 computations (33.3% saved)

simplify21.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 7 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	13	10
2	24	10
3	43	10
4	87	10
5	171	10
6	325	10
7	507	8
8	751	8
9	991	8
10	1049	8

Stop Event

1×

saturated

Counts

1 → 2

prune2.0ms (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 y x) -1/2 x)

Compiler

Compiled 31 to 19 computations (38.7% saved)

localize4.0ms (0.3%)

Local error

Found 1 expressions with local error:

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

series4.0ms (0.3%)

Counts

1 → 24

Calls

6 calls:

1.0ms	(fma.f64 (-.f64 y x) -1/2 x)	y	-inf
1.0ms	(fma.f64 (-.f64 y x) -1/2 x)	x	-inf
1.0ms	(fma.f64 (-.f64 y x) -1/2 x)	x	inf
1.0ms	(fma.f64 (-.f64 y x) -1/2 x)	y	0
1.0ms	(fma.f64 (-.f64 y x) -1/2 x)	y	inf

rewrite35.0ms (2.8%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	132	8
2	1720	8

Stop Event

1×	node limit

Counts

1 → 23

simplify21.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	204
1	18	168
2	30	168
3	44	168
4	68	168
5	104	168
6	173	168
7	246	168
8	307	168
9	395	168
10	445	168
11	449	168

Stop Event

1×

saturated

Counts

47 → 28

prune15.0ms (1.2%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	27	1	28
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	28	1	29

Error

Counts

29 → 1

Alt Table

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

Compiler

Compiled 302 to 167 computations (44.7% saved)

localize5.0ms (0.4%)

Local error

Found 1 expressions with local error:

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

series4.0ms (0.3%)

Counts

1 → 24

Calls

6 calls:

1.0ms	(fma.f64 3/2 x (*.f64 y -1/2))	x	-inf
1.0ms	(fma.f64 3/2 x (*.f64 y -1/2))	x	inf
1.0ms	(fma.f64 3/2 x (*.f64 y -1/2))	x	0
1.0ms	(fma.f64 3/2 x (*.f64 y -1/2))	y	-inf
1.0ms	(fma.f64 3/2 x (*.f64 y -1/2))	y	inf

rewrite35.0ms (2.8%)

Algorithm

1×	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`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	8
1	141	8
2	1541	8

Stop Event

1×	node limit

Counts

1 → 29

simplify22.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	204
1	18	168
2	30	168
3	44	168
4	68	168
5	104	168
6	173	168
7	246	168
8	307	168
9	395	168
10	445	168
11	449	168

Stop Event

1×

saturated

Counts

53 → 33

prune13.0ms (1.1%)

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)

regimes26.0ms (2.2%)

Accuracy

Total 0b remaining (0%)

Threshold costs 0b (0%)

Counts

7 → 1

Compiler

Compiled 177 to 128 computations (27.7% saved)

simplify4.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	8
1	8	8

Stop Event

1×

saturated

end39.0ms (3.2%)

Stop Event

1×

done

Compiler

Compiled 24 to 18 computations (25% saved)

Iter	Nodes	Cost
0	10	204
1	18	168
2	30	168
3	44	168
4	68	168
5	104	168
6	173	168
7	246	168
8	307	168
9	395	168
10	445	168
11	449	168

Iter	Nodes	Cost
0	10	204
1	18	168
2	30	168
3	44	168
4	68	168
5	104	168
6	173	168
7	246	168
8	307	168
9	395	168
10	445	168
11	449	168

Iter	Nodes	Cost
0	10	204
1	18	168
2	30	168
3	44	168
4	68	168
5	104	168
6	173	168
7	246	168
8	307	168
9	395	168
10	445	168
11	449	168

Iter	Nodes	Cost
0	10	204
1	18	168
2	30	168
3	44	168
4	68	168
5	104	168
6	173	168
7	246	168
8	307	168
9	395	168
10	445	168
11	449	168

Details

analyze49.0ms (4%)

sample894.0ms (72.9%)

preprocess34.0ms (2.8%)

simplify21.0ms (1.7%)

prune2.0ms (0.2%)

localize4.0ms (0.3%)

series4.0ms (0.3%)

rewrite35.0ms (2.8%)

simplify21.0ms (1.7%)

prune15.0ms (1.2%)

localize5.0ms (0.4%)

series4.0ms (0.3%)

rewrite35.0ms (2.8%)

simplify22.0ms (1.8%)

prune13.0ms (1.1%)

regimes26.0ms (2.2%)

simplify4.0ms (0.3%)

end39.0ms (3.2%)

Profiling

Iter	Nodes	Cost
0	10	204
1	18	168
2	30	168
3	44	168
4	68	168
5	104	168
6	173	168
7	246	168
8	307	168
9	395	168
10	445	168
11	449	168

Iter	Nodes	Cost
0	10	204
1	18	168
2	30	168
3	44	168
4	68	168
5	104	168
6	173	168
7	246	168
8	307	168
9	395	168
10	445	168
11	449	168