Details

analyze153.0ms (5%)

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
12.5%	87.4%	0.1%	5
31.2%	68.7%	0.1%	6
50%	50%	0.1%	7
67.1%	32.8%	0.1%	8
74.9%	25%	0.1%	9
83.9%	16%	0.1%	10
87.4%	12.5%	0.1%	11
92%	7.9%	0.1%	12
93.7%	6.2%	0.1%	13
96%	3.9%	0.1%	14

Compiler

Compiled 14 to 10 computations (28.6% saved)

sample1.2s (37.8%)

Results

821.0ms	8255×	body	128	valid
0.0ms	1×	body	2048	valid

Compiler

Compiled 41 to 29 computations (29.3% saved)

simplify215.0ms (7.1%)

Algorithm

1×	egg-herbie

Rules

2174×	`fma-neg_binary64`
1504×	`div-sub_binary64`
895×	`associate-/l/_binary64`
827×	`fma-def_binary64`
818×	`associate-/l*_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	10	16
1	18	16
2	28	14
3	41	14
4	57	14
5	91	14
6	134	14
7	193	14
8	356	14
9	521	14
10	825	14
11	1475	14
12	2002	14
13	1877	14
14	1931	14
15	1961	14
16	1967	14
17	1967	14
18	2590	14
19	2366	14
20	2366	14
21	3254	14
22	4052	14
23	4024	14
24	4504	14
25	4470	14
26	4706	14
27	4913	14

prune3.0ms (0.1%)

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

0.0b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.0b	(-.f64 x (/.f64 y (fma.f64 x (/.f64 y 2) 1)))

Compiler

Compiled 47 to 31 computations (34% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 x (/.f64 y (fma.f64 x (/.f64 y 2) 1)))
✓	8.3b	(/.f64 y (fma.f64 x (/.f64 y 2) 1))

series19.0ms (0.6%)

Counts

2 → 48

Calls

2 calls:

10.0ms	(-.f64 x (/.f64 y (fma.f64 x (/.f64 y 2) 1)))
9.0ms	(/.f64 y (fma.f64 x (/.f64 y 2) 1))

rewrite104.0ms (3.4%)

Algorithm

2×	batch-egg-rewrite

Rules

692×	`prod-diff_binary64`
218×	`fma-def_binary64`
184×	`egg-rr`
174×	`expm1-udef_binary64`
174×	`log1p-udef_binary64`

Counts

2 → 184

Calls

2 calls:

99.0ms	(-.f64 x (/.f64 y (fma.f64 x (/.f64 y 2) 1)))
99.0ms	(/.f64 y (fma.f64 x (/.f64 y 2) 1))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	25
1	198	25
2	2507	25
3	4853	25
4	5158	25
0	0	0
1	0	0

simplify71.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

930×	`times-frac_binary64`
635×	`fma-neg_binary64`
414×	`unswap-sqr_binary64`
402×	`distribute-rgt-neg-in_binary64`
392×	`distribute-lft-neg-in_binary64`

Counts

232 → 216

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	61	1030
1	199	1016
2	643	1006
3	2343	993
4	4887	993
5	6134	993

prune402.0ms (13.2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	214	2	216
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	214	3	217

Error

Counts

217 → 3

Alt Table

Status	Error	Program
	0.4b	(-.f64 x (*.f64 (cbrt.f64 (/.f64 y (fma.f64 x (/.f64 y 2) 1))) (pow.f64 (cbrt.f64 (/.f64 y (fma.f64 x (/.f64 y 2) 1))) 2)))
✓	0.0b	(-.f64 x (/.f64 y (fma.f64 x (/.f64 y 2) 1)))
▶	0.0b	(-.f64 x (pow.f64 (/.f64 (fma.f64 x (/.f64 y 2) 1) y) -1))

Compiler

Compiled 7150 to 4709 computations (34.1% saved)

localize8.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 x (pow.f64 (/.f64 (fma.f64 x (/.f64 y 2) 1) y) -1))
✓	0.1b	(pow.f64 (/.f64 (fma.f64 x (/.f64 y 2) 1) y) -1)
✓	8.2b	(/.f64 (fma.f64 x (/.f64 y 2) 1) y)

series28.0ms (0.9%)

Counts

3 → 72

Calls

3 calls:

11.0ms	(pow.f64 (/.f64 (fma.f64 x (/.f64 y 2) 1) y) -1)
10.0ms	(-.f64 x (pow.f64 (/.f64 (fma.f64 x (/.f64 y 2) 1) y) -1))
7.0ms	(/.f64 (fma.f64 x (/.f64 y 2) 1) y)

rewrite133.0ms (4.4%)

Algorithm

2×	batch-egg-rewrite

Rules

537×	`prod-diff_binary64`
219×	`egg-rr`
211×	`fma-def_binary64`
200×	`expm1-udef_binary64`
200×	`log1p-udef_binary64`

Counts

3 → 219

Calls

3 calls:

125.0ms	(-.f64 x (pow.f64 (/.f64 (fma.f64 x (/.f64 y 2) 1) y) -1))
125.0ms	(pow.f64 (/.f64 (fma.f64 x (/.f64 y 2) 1) y) -1)
125.0ms	(/.f64 (fma.f64 x (/.f64 y 2) 1) y)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	42
1	239	36
2	2857	36
3	4892	36
4	4924	36
0	0	0
1	0	0

simplify82.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

930×	`times-frac_binary64`
635×	`fma-neg_binary64`
414×	`unswap-sqr_binary64`
402×	`distribute-rgt-neg-in_binary64`
392×	`distribute-lft-neg-in_binary64`

Counts

291 → 255

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	64	1234
1	203	1184
2	647	1174
3	2347	1161
4	4891	1161
5	6138	1161

prune229.0ms (7.5%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	254	1	255
Fresh	1	0	1
Picked	1	0	1
Done	0	1	1
Total	256	2	258

Error

Counts

258 → 2

Alt Table

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

Compiler

Compiled 7803 to 5301 computations (32.1% saved)

localize7.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 x (pow.f64 (fma.f64 1/2 x (/.f64 1 y)) -1))
✓	0.1b	(pow.f64 (fma.f64 1/2 x (/.f64 1 y)) -1)

series22.0ms (0.7%)

Counts

2 → 48

Calls

2 calls:

13.0ms	(-.f64 x (pow.f64 (fma.f64 1/2 x (/.f64 1 y)) -1))
9.0ms	(pow.f64 (fma.f64 1/2 x (/.f64 1 y)) -1)

rewrite72.0ms (2.4%)

Algorithm

2×	batch-egg-rewrite

Rules

456×	`prod-diff_binary64`
417×	`log-prod_binary64`
192×	`fma-def_binary64`
177×	`expm1-udef_binary64`
177×	`log1p-udef_binary64`

Counts

2 → 122

Calls

2 calls:

69.0ms	(-.f64 x (pow.f64 (fma.f64 1/2 x (/.f64 1 y)) -1))
69.0ms	(pow.f64 (fma.f64 1/2 x (/.f64 1 y)) -1)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	25
1	212	25
2	2383	25
3	4914	25
0	0	0
1	0	0

simplify70.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

930×	`times-frac_binary64`
635×	`fma-neg_binary64`
414×	`unswap-sqr_binary64`
402×	`distribute-rgt-neg-in_binary64`
392×	`distribute-lft-neg-in_binary64`

Counts

170 → 154

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	61	1030
1	199	1016
2	643	1006
3	2343	993
4	4887	993
5	6134	993

prune123.0ms (4%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	154	0	154
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	154	2	156

Error

Counts

156 → 2

Alt Table

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

Compiler

Compiled 3743 to 2738 computations (26.9% saved)

regimes86.0ms (2.8%)

Accuracy

Total 0.0b remaining (90.5%)

Threshold costs 0.0b (90.5%)

Counts

23 → 1

Compiler

Compiled 908 to 647 computations (28.7% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	14
1	14	14
2	17	14
3	19	14
4	20	14
5	19	14

end55.0ms (1.8%)

Compiler: Compiled 48 to 35 computations (27.1% saved)

Details

analyze153.0ms (5%)

sample1.2s (37.8%)

simplify215.0ms (7.1%)

prune3.0ms (0.1%)

localize6.0ms (0.2%)

series19.0ms (0.6%)

rewrite104.0ms (3.4%)

simplify71.0ms (2.3%)

prune402.0ms (13.2%)

localize8.0ms (0.3%)

series28.0ms (0.9%)

rewrite133.0ms (4.4%)

simplify82.0ms (2.7%)

prune229.0ms (7.5%)

localize7.0ms (0.2%)

series22.0ms (0.7%)

rewrite72.0ms (2.4%)

simplify70.0ms (2.3%)

prune123.0ms (4%)

regimes86.0ms (2.8%)

simplify2.0ms (0.1%)

end55.0ms (1.8%)

Profiling