Details

analyze1.3s (26.4%)

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)

sample1.4s (28%)

Results

976.0ms	8256×	body	128	valid
323.0ms	2638×	body	128	invalid

Compiler

Compiled 44 to 29 computations (34.1% saved)

simplify64.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

783×	`fma-neg_binary64`
721×	`fma-def_binary64`
244×	`cancel-sign-sub-inv_binary64`
187×	`distribute-rgt-in_binary64`
138×	`distribute-lft-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	10	13
1	17	13
2	39	13
3	98	13
4	258	11
5	542	11
6	1019	11
7	1302	11
8	1414	11
9	1470	11
10	1476	11
11	1481	11
12	1481	11
13	1408	11

prune3.0ms (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
▶	6.3b	(fma.f64 y (/.f64 (-.f64 t z) a) x)
	6.4b	(-.f64 x (/.f64 (*.f64 y (-.f64 z t)) a))

Compiler

Compiled 76 to 46 computations (39.5% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 t z) a)
✓	6.0b	(fma.f64 y (/.f64 (-.f64 t z) a) x)

series35.0ms (0.7%)

Counts

2 → 88

Calls

2 calls:

25.0ms	(fma.f64 y (/.f64 (-.f64 t z) a) x)
10.0ms	(/.f64 (-.f64 t z) 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 t z) a)
113.0ms	(fma.f64 y (/.f64 (-.f64 t z) 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

simplify90.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

1054×	`fma-def_binary64`
632×	`fma-neg_binary64`
166×	`cancel-sign-sub-inv_binary64`
157×	`distribute-rgt-in_binary64`
157×	`unsub-neg_binary64`

Counts

212 → 143

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	31	944
1	71	944
2	151	908
3	286	774
4	539	774
5	963	774
6	1262	774
7	1395	774
8	1476	774
9	1485	774
10	1485	774
11	1412	774

prune82.0ms (1.6%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	139	4	143
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	140	5	145

Error

Counts

145 → 5

Alt Table

Status	Error	Program
	6.3b	(fma.f64 y (pow.f64 (/.f64 a (-.f64 t z)) -1) x)
▶	1.4b	(fma.f64 (-.f64 t z) (/.f64 y a) x)
	6.4b	(-.f64 (+.f64 (/.f64 (.f64 y t) a) x) (/.f64 (.f64 y z) a))
	37.5b	(pow.f64 (sqrt.f64 (fma.f64 y (/.f64 (-.f64 t z) a) x)) 2)
✓	6.3b	(fma.f64 y (/.f64 (-.f64 t z) a) x)

Compiler

Compiled 2850 to 709 computations (75.1% saved)

localize7.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

series21.0ms (0.4%)

Counts

1 → 60

Calls

1 calls:

21.0ms

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

rewrite50.0ms (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:

49.0ms

(fma.f64 (-.f64 t z) (/.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

simplify95.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

899×	`fma-def_binary64`
670×	`fma-neg_binary64`
186×	`cancel-sign-sub-inv_binary64`
109×	`distribute-rgt-in_binary64`
103×	`associate-/l*_binary64`

Counts

90 → 44

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	27	694
1	59	694
2	125	680
3	241	590
4	426	590
5	708	590
6	1173	590
7	1323	590
8	1418	590
9	1459	590
10	1465	590
11	1470	590
12	1470	590
13	1397	590

prune20.0ms (0.4%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	43	1	44
Fresh	1	2	3
Picked	0	1	1
Done	0	1	1
Total	44	5	49

Error

Counts

49 → 5

Alt Table

Status	Error	Program
▶	6.3b	(fma.f64 y (pow.f64 (/.f64 a (-.f64 t z)) -1) x)
✓	1.4b	(fma.f64 (-.f64 t z) (/.f64 y a) x)
	6.4b	(-.f64 (+.f64 (/.f64 (.f64 y t) a) x) (/.f64 (.f64 y z) a))
	34.7b	(pow.f64 (sqrt.f64 (fma.f64 (-.f64 t z) (/.f64 y a) x)) 2)
✓	6.3b	(fma.f64 y (/.f64 (-.f64 t z) a) x)

Compiler

Compiled 679 to 203 computations (70.1% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 a (-.f64 t z))
✓	0.8b	(pow.f64 (/.f64 a (-.f64 t z)) -1)
✓	6.0b	(fma.f64 y (pow.f64 (/.f64 a (-.f64 t z)) -1) x)

series188.0ms (3.8%)

Counts

3 → 120

Calls

3 calls:

97.0ms	(fma.f64 y (pow.f64 (/.f64 a (-.f64 t z)) -1) x)
75.0ms	(pow.f64 (/.f64 a (-.f64 t z)) -1)
15.0ms	(/.f64 a (-.f64 t z))

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

simplify94.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

483×	`associate-/r/_binary64`
401×	`cancel-sign-sub-inv_binary64`
381×	`associate-/l/_binary64`
338×	`unswap-sqr_binary64`
280×	`fma-neg_binary64`

Counts

228 → 140

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	67	1528
1	174	1528
2	486	1328
3	1920	1289
4	4346	1289
5	5132	1289

prune194.0ms (3.9%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	140	0	140
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	140	5	145

Error

Counts

145 → 5

Alt Table

Status	Error	Program
✓	6.3b	(fma.f64 y (pow.f64 (/.f64 a (-.f64 t z)) -1) x)
✓	1.4b	(fma.f64 (-.f64 t z) (/.f64 y a) x)
▶	6.4b	(-.f64 (+.f64 (/.f64 (.f64 y t) a) x) (/.f64 (.f64 y z) a))
	34.7b	(pow.f64 (sqrt.f64 (fma.f64 (-.f64 t z) (/.f64 y a) x)) 2)
✓	6.3b	(fma.f64 y (/.f64 (-.f64 t z) a) x)

Compiler

Compiled 2109 to 766 computations (63.7% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (/.f64 (*.f64 y t) a) x)
✓	5.7b	(/.f64 (*.f64 y t) a)
✓	5.9b	(/.f64 (*.f64 y z) a)

series38.0ms (0.8%)

Counts

3 → 30

Calls

3 calls:

13.0ms	(/.f64 (*.f64 y t) a)
13.0ms	(+.f64 (/.f64 (*.f64 y t) a) x)
12.0ms	(/.f64 (*.f64 y z) a)

rewrite67.0ms (1.3%)

Algorithm

2×	batch-egg-rewrite

Rules

854×	`prod-diff_binary64`
125×	`add-sqr-sqrt_binary64`
124×	`egg-rr`
117×	`log1p-expm1-u_binary64`
117×	`expm1-log1p-u_binary64`

Counts

3 → 124

Calls

3 calls:

65.0ms	(+.f64 (/.f64 (*.f64 y t) a) x)
65.0ms	(/.f64 (*.f64 y t) a)
65.0ms	(/.f64 (*.f64 y z) a)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	24
1	240	24
2	3419	24
3	5090	24
0	0	0
1	0	0

simplify16.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

4×	`fma-def_binary64`
3×	`*-commutative_binary64`
2×	`associate-/l*_binary64`
2×	`associate-/r/_binary64`
1×	`+-commutative_binary64`

Counts

154 → 127

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	8	228
1	12	228
2	16	192
3	20	192
4	23	192
5	24	192
6	24	192

prune75.0ms (1.5%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	127	0	127
Fresh	0	1	1
Picked	0	1	1
Done	0	3	3
Total	127	5	132

Error

Counts

132 → 5

Alt Table

Status	Error	Program
✓	6.3b	(fma.f64 y (pow.f64 (/.f64 a (-.f64 t z)) -1) x)
✓	1.4b	(fma.f64 (-.f64 t z) (/.f64 y a) x)
✓	6.4b	(-.f64 (+.f64 (/.f64 (.f64 y t) a) x) (/.f64 (.f64 y z) a))
	34.7b	(pow.f64 (sqrt.f64 (fma.f64 (-.f64 t z) (/.f64 y a) x)) 2)
✓	6.3b	(fma.f64 y (/.f64 (-.f64 t z) a) x)

Compiler

Compiled 2432 to 653 computations (73.1% saved)

regimes750.0ms (15%)

Accuracy

Total 0.7b remaining (97.3%)

Threshold costs 0.7b (97.3%)

Counts

32 → 3

Compiler

Compiled 4417 to 2921 computations (33.9% saved)

bsearch1.0ms (0%)

Compiler: Compiled 10 to 7 computations (30% saved)

simplify12.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

51×	`distribute-rgt-neg-in_binary64`
37×	`distribute-lft-neg-in_binary64`
37×	`cancel-sign-sub-inv_binary64`
33×	`neg-sub0_binary64`
33×	`neg-mul-1_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	30	72
1	50	72
2	72	70
3	98	70
4	122	70
5	141	70
6	156	70
7	173	70
8	192	70
9	218	70
10	244	70
11	265	70
12	272	70
13	274	70
14	270	70

end157.0ms (3.1%)

Compiler: Compiled 181 to 102 computations (43.6% saved)

Iter	Nodes	Cost
0	30	72
1	50	72
2	72	70
3	98	70
4	122	70
5	141	70
6	156	70
7	173	70
8	192	70
9	218	70
10	244	70
11	265	70
12	272	70
13	274	70
14	270	70

Iter	Nodes	Cost
0	30	72
1	50	72
2	72	70
3	98	70
4	122	70
5	141	70
6	156	70
7	173	70
8	192	70
9	218	70
10	244	70
11	265	70
12	272	70
13	274	70
14	270	70

Details

analyze1.3s (26.4%)

sample1.4s (28%)

simplify64.0ms (1.3%)

prune3.0ms (0.1%)

localize6.0ms (0.1%)

series35.0ms (0.7%)

rewrite116.0ms (2.3%)

simplify90.0ms (1.8%)

prune82.0ms (1.6%)

localize7.0ms (0.1%)

series21.0ms (0.4%)

rewrite50.0ms (1%)

simplify95.0ms (1.9%)

prune20.0ms (0.4%)

localize7.0ms (0.1%)

series188.0ms (3.8%)

rewrite89.0ms (1.8%)

simplify94.0ms (1.9%)

prune194.0ms (3.9%)

localize9.0ms (0.2%)

series38.0ms (0.8%)

rewrite67.0ms (1.3%)

simplify16.0ms (0.3%)

prune75.0ms (1.5%)

regimes750.0ms (15%)

bsearch1.0ms (0%)

simplify12.0ms (0.2%)

end157.0ms (3.1%)

Profiling

Iter	Nodes	Cost
0	30	72
1	50	72
2	72	70
3	98	70
4	122	70
5	141	70
6	156	70
7	173	70
8	192	70
9	218	70
10	244	70
11	265	70
12	272	70
13	274	70
14	270	70