Details

analyze56.0ms (1.4%)

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
25%	74.9%	0.1%	3
25%	74.9%	0.1%	4
56.2%	43.7%	0.1%	5
65.6%	34.3%	0.1%	6
79.6%	20.3%	0.1%	7
83.5%	16.4%	0.1%	8
90.1%	9.8%	0.1%	9
91.9%	8%	0.1%	10
95.1%	4.8%	0.1%	11
96%	4%	0.1%	12
97.5%	2.4%	0.1%	13
97.9%	2%	0.1%	14

Compiler

Compiled 12 to 8 computations (33.3% saved)

sample1.1s (25.6%)

Results

750.0ms

8256×

body

128

valid

Compiler

Compiled 35 to 23 computations (34.3% saved)

simplify272.0ms (6.6%)

Algorithm

1×	egg-herbie

Rules

1222×	`fma-neg_binary64`
983×	`fma-def_binary64`
688×	`div-sub_binary64`
423×	`sub-neg_binary64`
412×	`distribute-rgt-in_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	13
1	18	13
2	35	13
3	74	13
4	151	13
5	245	13
6	641	13
7	1125	13
8	2158	13
9	2729	13
10	3037	13
11	2995	13
12	3049	13
13	3063	13
14	3569	13
15	3559	13
16	3559	13
17	3559	13
18	3559	13
19	3559	13
20	3655	13
21	3703	13
22	3785	13
23	3593	13

prune2.0ms (0.1%)

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 2 (+.f64 x y)))

Compiler

Compiled 33 to 21 computations (36.4% saved)

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

series16.0ms (0.4%)

Counts

1 → 24

Calls

1 calls:

16.0ms

(/.f64 (-.f64 x y) (-.f64 2 (+.f64 x y)))

rewrite132.0ms (3.2%)

Algorithm

2×	batch-egg-rewrite

Rules

843×	`prod-diff_binary64`
233×	`egg-rr`
189×	`log1p-udef_binary64`
103×	`add-sqr-sqrt_binary64`
100×	`log1p-expm1-u_binary64`

Counts

1 → 233

Calls

1 calls:

120.0ms

(/.f64 (-.f64 x y) (-.f64 2 (+.f64 x y)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	13
1	197	13
2	2938	13
3	4979	13
0	0	0
1	0	0

simplify71.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

593×	`fma-def_binary64`
491×	`times-frac_binary64`
377×	`associate-/l*_binary64`
363×	`fma-neg_binary64`
349×	`associate-/r*_binary64`

Counts

257 → 262

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	132	1038
1	412	1030
2	1562	918
3	4954	918
4	5192	918

prune305.0ms (7.4%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	258	4	262
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	259	4	263

Error

Counts

263 → 4

Alt Table

Status	Error	Program
	29.2b	(*.f64 (/.f64 (-.f64 x y) (-.f64 4 (pow.f64 (+.f64 x y) 2))) (+.f64 2 (+.f64 x y)))
	40.2b	(+.f64 (fma.f64 2 (/.f64 y x) -1) (/.f64 -2 x))
▶	0.0b	(-.f64 (/.f64 x (-.f64 2 (+.f64 x y))) (/.f64 y (-.f64 2 (+.f64 x y))))
	0.1b	(pow.f64 (/.f64 (-.f64 2 (+.f64 x y)) (-.f64 x y)) -1)

Compiler

Compiled 15341 to 8660 computations (43.5% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

series50.0ms (1.2%)

Counts

3 → 72

Calls

3 calls:

22.0ms	(-.f64 (/.f64 x (-.f64 2 (+.f64 x y))) (/.f64 y (-.f64 2 (+.f64 x y))))
14.0ms	(/.f64 y (-.f64 2 (+.f64 x y)))
14.0ms	(/.f64 x (-.f64 2 (+.f64 x y)))

rewrite100.0ms (2.4%)

Algorithm

2×	batch-egg-rewrite

Rules

542×	`fma-def_binary64`
278×	`fma-neg_binary64`
227×	`egg-rr`
221×	`expm1-udef_binary64`
221×	`log1p-udef_binary64`

Counts

3 → 227

Calls

3 calls:

94.0ms	(/.f64 x (-.f64 2 (+.f64 x y)))
94.0ms	(-.f64 (/.f64 x (-.f64 2 (+.f64 x y))) (/.f64 y (-.f64 2 (+.f64 x y))))
94.0ms	(/.f64 y (-.f64 2 (+.f64 x y)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	33
1	229	33
2	3601	33
3	5076	33
0	0	0
1	0	0

simplify81.0ms (2%)

Algorithm

1×	egg-herbie

Rules

820×	`times-frac_binary64`
392×	`sub-neg_binary64`
331×	`cancel-sign-sub-inv_binary64`
226×	`associate-+r+_binary64`
214×	`+-commutative_binary64`

Counts

299 → 309

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	227	2940
1	761	2912
2	2929	2846
3	5001	2846

prune244.0ms (6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	309	0	309
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	309	4	313

Error

Counts

313 → 4

Alt Table

Status	Error	Program
	29.2b	(*.f64 (/.f64 (-.f64 x y) (-.f64 4 (pow.f64 (+.f64 x y) 2))) (+.f64 2 (+.f64 x y)))
	40.2b	(+.f64 (fma.f64 2 (/.f64 y x) -1) (/.f64 -2 x))
✓	0.0b	(-.f64 (/.f64 x (-.f64 2 (+.f64 x y))) (/.f64 y (-.f64 2 (+.f64 x y))))
▶	0.1b	(pow.f64 (/.f64 (-.f64 2 (+.f64 x y)) (-.f64 x y)) -1)

Compiler

Compiled 9287 to 5123 computations (44.8% saved)

localize7.0ms (0.2%)

Local error

Found 2 expressions with local error:

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

series68.0ms (1.6%)

Counts

2 → 48

Calls

2 calls:

52.0ms	(pow.f64 (/.f64 (-.f64 2 (+.f64 x y)) (-.f64 x y)) -1)
16.0ms	(/.f64 (-.f64 2 (+.f64 x y)) (-.f64 x y))

rewrite100.0ms (2.4%)

Algorithm

2×	batch-egg-rewrite

Rules

722×	`prod-diff_binary64`
215×	`log1p-udef_binary64`
170×	`egg-rr`
121×	`add-sqr-sqrt_binary64`
117×	`log1p-expm1-u_binary64`

Counts

2 → 170

Calls

2 calls:

93.0ms	(/.f64 (-.f64 2 (+.f64 x y)) (-.f64 x y))
93.0ms	(pow.f64 (/.f64 (-.f64 2 (+.f64 x y)) (-.f64 x y)) -1)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	29
1	238	26
2	3277	26
3	5095	26
0	0	0
1	0	0

simplify76.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

500×	`cancel-sign-sub-inv_binary64`
372×	`sub-neg_binary64`
345×	`fma-def_binary64`
268×	`times-frac_binary64`
265×	`associate-+r+_binary64`

Counts

218 → 227

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	276	2396
1	955	2348
2	4006	2299
3	5328	2299

prune186.0ms (4.5%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	226	1	227
Fresh	1	1	2
Picked	1	0	1
Done	0	1	1
Total	228	3	231

Error

Counts

231 → 3

Alt Table

Status	Error	Program
	29.2b	(*.f64 (/.f64 (-.f64 x y) (-.f64 4 (pow.f64 (+.f64 x y) 2))) (+.f64 2 (+.f64 x y)))
▶	0.1b	(pow.f64 (-.f64 (/.f64 (-.f64 2 x) (-.f64 x y)) (/.f64 y (-.f64 x y))) -1)
✓	0.0b	(-.f64 (/.f64 x (-.f64 2 (+.f64 x y))) (/.f64 y (-.f64 2 (+.f64 x y))))

Compiler

Compiled 9843 to 4247 computations (56.9% saved)

localize7.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series117.0ms (2.8%)

Counts

4 → 96

Calls

4 calls:

66.0ms	(pow.f64 (-.f64 (/.f64 (-.f64 2 x) (-.f64 x y)) (/.f64 y (-.f64 x y))) -1)
21.0ms	(-.f64 (/.f64 (-.f64 2 x) (-.f64 x y)) (/.f64 y (-.f64 x y)))
20.0ms	(/.f64 (-.f64 2 x) (-.f64 x y))
9.0ms	(/.f64 y (-.f64 x y))

rewrite102.0ms (2.5%)

Algorithm

2×	batch-egg-rewrite

Rules

365×	`fma-neg_binary64`
253×	`expm1-udef_binary64`
253×	`log1p-udef_binary64`
191×	`egg-rr`
140×	`add-sqr-sqrt_binary64`

Counts

4 → 191

Calls

4 calls:

98.0ms	(/.f64 y (-.f64 x y))
98.0ms	(/.f64 (-.f64 2 x) (-.f64 x y))
98.0ms	(-.f64 (/.f64 (-.f64 2 x) (-.f64 x y)) (/.f64 y (-.f64 x y)))
98.0ms	(pow.f64 (-.f64 (/.f64 (-.f64 2 x) (-.f64 x y)) (/.f64 y (-.f64 x y))) -1)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	46
1	271	46
2	4094	46
3	5192	46
0	0	0
1	0	0

simplify104.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

363×	`fma-neg_binary64`
358×	`fma-def_binary64`
301×	`associate-+r+_binary64`
293×	`+-commutative_binary64`
284×	`times-frac_binary64`

Counts

287 → 290

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	332	4068
1	1131	3993
2	4902	3990
3	5198	3990

prune253.0ms (6.2%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	290	0	290
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	290	3	293

Error

Counts

293 → 3

Alt Table

Status	Error	Program
	29.2b	(*.f64 (/.f64 (-.f64 x y) (-.f64 4 (pow.f64 (+.f64 x y) 2))) (+.f64 2 (+.f64 x y)))
✓	0.1b	(pow.f64 (-.f64 (/.f64 (-.f64 2 x) (-.f64 x y)) (/.f64 y (-.f64 x y))) -1)
✓	0.0b	(-.f64 (/.f64 x (-.f64 2 (+.f64 x y))) (/.f64 y (-.f64 2 (+.f64 x y))))

Compiler

Compiled 8939 to 5212 computations (41.7% saved)

regimes591.0ms (14.4%)

Accuracy

Total 0.0b remaining (64.5%)

Threshold costs 0.0b (64.5%)

Counts

145 → 1

Compiler

Compiled 6910 to 4944 computations (28.5% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	22
1	14	22
2	27	22
3	37	22
4	43	22
5	45	22
6	45	22

end96.0ms (2.3%)

Compiler: Compiled 87 to 52 computations (40.2% saved)

Details

analyze56.0ms (1.4%)

sample1.1s (25.6%)

simplify272.0ms (6.6%)

prune2.0ms (0.1%)

localize5.0ms (0.1%)

series16.0ms (0.4%)

rewrite132.0ms (3.2%)

simplify71.0ms (1.7%)

prune305.0ms (7.4%)

localize6.0ms (0.1%)

series50.0ms (1.2%)

rewrite100.0ms (2.4%)

simplify81.0ms (2%)

prune244.0ms (6%)

localize7.0ms (0.2%)

series68.0ms (1.6%)

rewrite100.0ms (2.4%)

simplify76.0ms (1.9%)

prune186.0ms (4.5%)

localize7.0ms (0.2%)

series117.0ms (2.8%)

rewrite102.0ms (2.5%)

simplify104.0ms (2.5%)

prune253.0ms (6.2%)

regimes591.0ms (14.4%)

simplify3.0ms (0.1%)

end96.0ms (2.3%)

Profiling