Details

analyze1.2s (23.5%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
0%	99.8%	0.2%	9
0%	99.8%	0.2%	10
10.1%	89.6%	0.2%	11
15.2%	84.6%	0.2%	12
20.5%	79.3%	0.2%	13
21.6%	77.1%	1.3%	14

Compiler

Compiled 15 to 10 computations (33.3% saved)

sample1.6s (33.1%)

Results

1.1s	8256×	body	128	valid
369.0ms	2555×	body	128	invalid

Compiler

Compiled 44 to 29 computations (34.1% saved)

simplify65.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

946×	`fma-def_binary64`
719×	`fma-neg_binary64`
235×	`cancel-sign-sub-inv_binary64`
163×	`distribute-rgt-in_binary64`
116×	`distribute-lft-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	10	13
1	16	13
2	31	11
3	62	11
4	130	11
5	231	11
6	390	11
7	639	11
8	955	11
9	1272	11
10	1381	11
11	1449	11
12	1474	11
13	1471	11
14	1471	11
15	1398	11

prune4.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

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

Error

0.1b

Counts

3 → 2

Alt Table

Status	Error	Program
	5.9b	(+.f64 x (/.f64 (*.f64 y (-.f64 z t)) a))
▶	5.6b	(fma.f64 y (/.f64 (-.f64 z t) a) x)

Compiler

Compiled 76 to 45 computations (40.8% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 z t) a)
✓	5.3b	(fma.f64 y (/.f64 (-.f64 z t) a) x)

series42.0ms (0.9%)

Counts

2 → 88

Calls

2 calls:

34.0ms	(fma.f64 y (/.f64 (-.f64 z t) a) x)
9.0ms	(/.f64 (-.f64 z t) a)

rewrite116.0ms (2.3%)

Algorithm

2×	batch-egg-rewrite

Rules

610×	`prod-diff_binary64`
478×	`fma-udef_binary64`
280×	`fma-def_binary64`
194×	`fma-neg_binary64`
192×	`expm1-udef_binary64`

Counts

2 → 124

Calls

2 calls:

113.0ms	(/.f64 (-.f64 z t) a)
113.0ms	(fma.f64 y (/.f64 (-.f64 z t) a) x)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	18
1	197	18
2	2709	18
3	4777	18
4	4727	18
5	5047	18
0	0	0
1	0	0

simplify115.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

961×	`fma-def_binary64`
643×	`fma-neg_binary64`
172×	`cancel-sign-sub-inv_binary64`
155×	`unsub-neg_binary64`
154×	`distribute-rgt-in_binary64`

Counts

212 → 142

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	29	1214
1	71	944
2	154	908
3	292	774
4	563	774
5	968	774
6	1258	774
7	1393	774
8	1474	774
9	1483	774
10	1483	774
11	1410	774

prune84.0ms (1.7%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	137	5	142
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	139	5	144

Error

0.0b

Counts

144 → 5

Alt Table

Status	Error	Program
	5.6b	(fma.f64 y (*.f64 (-.f64 z t) (/.f64 1 a)) x)
▶	1.3b	(fma.f64 (-.f64 z t) (/.f64 y a) x)
	35.6b	(fma.f64 y (.f64 (sqrt.f64 (-.f64 z t)) (.f64 (sqrt.f64 (-.f64 z t)) (/.f64 1 a))) x)
	5.9b	(-.f64 (+.f64 (/.f64 (.f64 y z) a) x) (/.f64 (.f64 y t) a))
	5.6b	(fma.f64 y (pow.f64 (/.f64 a (-.f64 z t)) -1) x)

Compiler

Compiled 2864 to 721 computations (74.8% saved)

localize6.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	1.3b	(fma.f64 (-.f64 z t) (/.f64 y a) x)

series23.0ms (0.5%)

Counts

1 → 60

Calls

1 calls:

23.0ms

(fma.f64 (-.f64 z t) (/.f64 y a) x)

rewrite156.0ms (3.1%)

Algorithm

2×	batch-egg-rewrite

Rules

499×	`log-prod_binary64`
446×	`prod-diff_binary64`
200×	`fma-def_binary64`
188×	`expm1-udef_binary64`
188×	`log1p-udef_binary64`

Counts

1 → 30

Calls

1 calls:

155.0ms

(fma.f64 (-.f64 z t) (/.f64 y a) x)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	11
1	194	11
2	2576	11
3	5412	11
0	0	0
1	0	0

simplify92.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

708×	`fma-def_binary64`
691×	`fma-neg_binary64`
198×	`cancel-sign-sub-inv_binary64`
102×	`div-sub_binary64`
93×	`associate-r_binary64`

Counts

90 → 43

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	25	964
1	58	694
2	125	680
3	237	590
4	431	590
5	712	590
6	1161	590
7	1329	590
8	1418	590
9	1454	590
10	1460	590
11	1465	590
12	1465	590
13	1392	590

prune22.0ms (0.4%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	43	0	43
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	43	5	48

Error

0.0b

Counts

48 → 5

Alt Table

Status	Error	Program
	5.6b	(fma.f64 y (*.f64 (-.f64 z t) (/.f64 1 a)) x)
✓	1.3b	(fma.f64 (-.f64 z t) (/.f64 y a) x)
	35.6b	(fma.f64 y (.f64 (sqrt.f64 (-.f64 z t)) (.f64 (sqrt.f64 (-.f64 z t)) (/.f64 1 a))) x)
	5.9b	(-.f64 (+.f64 (/.f64 (.f64 y z) a) x) (/.f64 (.f64 y t) a))
▶	5.6b	(fma.f64 y (pow.f64 (/.f64 a (-.f64 z t)) -1) x)

Compiler

Compiled 693 to 215 computations (69% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 a (-.f64 z t))
✓	0.7b	(pow.f64 (/.f64 a (-.f64 z t)) -1)
✓	5.3b	(fma.f64 y (pow.f64 (/.f64 a (-.f64 z t)) -1) x)

series255.0ms (5.2%)

Counts

3 → 120

Calls

3 calls:

175.0ms	(fma.f64 y (pow.f64 (/.f64 a (-.f64 z t)) -1) x)
64.0ms	(pow.f64 (/.f64 a (-.f64 z t)) -1)
17.0ms	(/.f64 a (-.f64 z t))

rewrite89.0ms (1.8%)

Algorithm

2×	batch-egg-rewrite

Rules

498×	`prod-diff_binary64`
215×	`expm1-udef_binary64`
215×	`log1p-udef_binary64`
204×	`fma-def_binary64`
193×	`log-pow_binary64`

Counts

3 → 108

Calls

3 calls:

87.0ms	(/.f64 a (-.f64 z t))
87.0ms	(pow.f64 (/.f64 a (-.f64 z t)) -1)
87.0ms	(fma.f64 y (pow.f64 (/.f64 a (-.f64 z t)) -1) x)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	31
1	236	25
2	2957	25
3	4929	25
4	5005	25
0	0	0
1	0	0

simplify78.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

606×	`fma-neg_binary64`
567×	`cancel-sign-sub-inv_binary64`
426×	`associate-/l/_binary64`
192×	`times-frac_binary64`
191×	`neg-mul-1_binary64`

Counts

228 → 139

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	65	1798
1	173	1528
2	489	1418
3	2034	1376
4	4588	1376
5	4989	1376

prune113.0ms (2.3%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	138	1	139
Fresh	2	1	3
Picked	0	1	1
Done	0	1	1
Total	140	4	144

Error

0.0b

Counts

144 → 4

Alt Table

Status	Error	Program
✓	1.3b	(fma.f64 (-.f64 z t) (/.f64 y a) x)
	5.9b	(-.f64 (+.f64 (/.f64 (.f64 y z) a) x) (/.f64 (.f64 y t) a))
▶	5.7b	(fma.f64 y (/.f64 (/.f64 1 a) (/.f64 1 (-.f64 z t))) x)
✓	5.6b	(fma.f64 y (pow.f64 (/.f64 a (-.f64 z t)) -1) x)

Compiler

Compiled 2085 to 761 computations (63.5% saved)

localize55.0ms (1.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 1 (-.f64 z t))
✓	0.3b	(/.f64 (/.f64 1 a) (/.f64 1 (-.f64 z t)))
✓	5.3b	(fma.f64 y (/.f64 (/.f64 1 a) (/.f64 1 (-.f64 z t))) x)

series40.0ms (0.8%)

Counts

3 → 120

Calls

3 calls:

24.0ms	(fma.f64 y (/.f64 (/.f64 1 a) (/.f64 1 (-.f64 z t))) x)
10.0ms	(/.f64 (/.f64 1 a) (/.f64 1 (-.f64 z t)))
7.0ms	(/.f64 1 (-.f64 z t))

rewrite65.0ms (1.3%)

Algorithm

2×	batch-egg-rewrite

Rules

460×	`prod-diff_binary64`
232×	`expm1-udef_binary64`
232×	`log1p-udef_binary64`
218×	`fma-def_binary64`
133×	`add-sqr-sqrt_binary64`

Counts

3 → 91

Calls

3 calls:

64.0ms	(/.f64 1 (-.f64 z t))
64.0ms	(/.f64 (/.f64 1 a) (/.f64 1 (-.f64 z t)))
64.0ms	(fma.f64 y (/.f64 (/.f64 1 a) (/.f64 1 (-.f64 z t))) x)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	37
1	261	25
2	3256	25
3	4952	25
0	0	0
1	0	0

simplify76.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

547×	`fma-def_binary64`
506×	`fma-neg_binary64`
483×	`associate-/l*_binary64`
410×	`associate-/r*_binary64`
262×	`associate-*l/_binary64`

Counts

211 → 124

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	64	1684
1	164	1396
2	415	1358
3	1240	1247
4	4364	1235
5	4985	1235

prune75.0ms (1.5%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	124	0	124
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	124	4	128

Error

0.0b

Counts

128 → 4

Alt Table

Status	Error	Program
✓	1.3b	(fma.f64 (-.f64 z t) (/.f64 y a) x)
	5.9b	(-.f64 (+.f64 (/.f64 (.f64 y z) a) x) (/.f64 (.f64 y t) a))
✓	5.7b	(fma.f64 y (/.f64 (/.f64 1 a) (/.f64 1 (-.f64 z t))) x)
✓	5.6b	(fma.f64 y (pow.f64 (/.f64 a (-.f64 z t)) -1) x)

Compiler

Compiled 1838 to 799 computations (56.5% saved)

regimes499.0ms (10.1%)

Accuracy

Total 2.4b remaining (98.9%)

Threshold costs 0b (0%)

Counts

47 → 1

Compiler

Compiled 6478 to 4209 computations (35% saved)

simplify2.0ms (0%)

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	9	11
1	11	11
2	16	11
3	18	11
4	19	11
5	19	11

end66.0ms (1.3%)

Compiler: Compiled 89 to 57 computations (36% saved)

Details

analyze1.2s (23.5%)

sample1.6s (33.1%)

simplify65.0ms (1.3%)

prune4.0ms (0.1%)

localize6.0ms (0.1%)

series42.0ms (0.9%)

rewrite116.0ms (2.3%)

simplify115.0ms (2.3%)

prune84.0ms (1.7%)

localize6.0ms (0.1%)

series23.0ms (0.5%)

rewrite156.0ms (3.1%)

simplify92.0ms (1.9%)

prune22.0ms (0.4%)

localize7.0ms (0.1%)

series255.0ms (5.2%)

rewrite89.0ms (1.8%)

simplify78.0ms (1.6%)

prune113.0ms (2.3%)

localize55.0ms (1.1%)

series40.0ms (0.8%)

rewrite65.0ms (1.3%)

simplify76.0ms (1.5%)

prune75.0ms (1.5%)

regimes499.0ms (10.1%)

simplify2.0ms (0%)

end66.0ms (1.3%)

Profiling