Details

analyze2.4s (26.7%)

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)

sample2.6s (29.1%)

Results

1.8s	8256×	body	128	valid
605.0ms	2644×	body	128	invalid

Compiler

Compiled 44 to 29 computations (34.1% saved)

simplify76.0ms (0.8%)

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

prune6.0ms (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
▶	6.5b	(fma.f64 y (/.f64 (-.f64 t z) a) x)
	7.7b	(-.f64 x (/.f64 (*.f64 y (-.f64 z t)) a))

Compiler

Compiled 76 to 46 computations (39.5% saved)

localize12.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 t z) a)
✓	6.1b	(fma.f64 y (/.f64 (-.f64 t z) a) x)

series115.0ms (1.3%)

Counts

2 → 88

Calls

2 calls:

62.0ms	(/.f64 (-.f64 t z) a)
53.0ms	(fma.f64 y (/.f64 (-.f64 t z) a) x)

rewrite153.0ms (1.7%)

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 → 122

Calls

2 calls:

150.0ms	(/.f64 (-.f64 t z) a)
150.0ms	(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

simplify100.0ms (1.1%)

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

210 → 142

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

prune152.0ms (1.7%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	139	3	142
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	139	5	144

Error

0.0b

Counts

144 → 5

Alt Table

Status	Error	Program
	35.9b	(pow.f64 (sqrt.f64 (fma.f64 y (/.f64 (-.f64 t z) a) x)) 2)
	7.6b	(*.f64 (cbrt.f64 (fma.f64 y (/.f64 (-.f64 t z) a) x)) (pow.f64 (cbrt.f64 (fma.f64 y (/.f64 (-.f64 t z) a) x)) 2))
✓	6.5b	(fma.f64 y (/.f64 (-.f64 t z) a) x)
	7.7b	(-.f64 x (/.f64 (*.f64 y (-.f64 z t)) a))
▶	2.4b	(fma.f64 (-.f64 t z) (/.f64 y a) x)

Compiler

Compiled 2856 to 709 computations (75.2% saved)

localize6.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	2.2b	(fma.f64 (-.f64 t z) (/.f64 y a) x)

series51.0ms (0.6%)

Counts

1 → 60

Calls

1 calls:

51.0ms

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

rewrite52.0ms (0.6%)

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 → 29

Calls

1 calls:

51.0ms

(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

simplify101.0ms (1.1%)

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

89 → 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

prune18.0ms (0.2%)

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

0.0b

Counts

49 → 5

Alt Table

Status	Error	Program
	33.3b	(pow.f64 (sqrt.f64 (fma.f64 (-.f64 t z) (/.f64 y a) x)) 2)
▶	7.6b	(*.f64 (cbrt.f64 (fma.f64 y (/.f64 (-.f64 t z) a) x)) (pow.f64 (cbrt.f64 (fma.f64 y (/.f64 (-.f64 t z) a) x)) 2))
✓	6.5b	(fma.f64 y (/.f64 (-.f64 t z) a) x)
	7.7b	(-.f64 x (/.f64 (*.f64 y (-.f64 z t)) a))
✓	2.4b	(fma.f64 (-.f64 t z) (/.f64 y a) x)

Compiler

Compiled 693 to 203 computations (70.7% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(*.f64 (cbrt.f64 (fma.f64 y (/.f64 (-.f64 t z) a) x)) (pow.f64 (cbrt.f64 (fma.f64 y (/.f64 (-.f64 t z) a) x)) 2))
✓	0.4b	(pow.f64 (cbrt.f64 (fma.f64 y (/.f64 (-.f64 t z) a) x)) 2)
✓	0.5b	(cbrt.f64 (fma.f64 y (/.f64 (-.f64 t z) a) x))
	6.1b	(fma.f64 y (/.f64 (-.f64 t z) a) x)

series733.0ms (8.2%)

Counts

3 → 180

Calls

3 calls:

492.0ms

(pow.f64 (cbrt.f64 (fma.f64 y (/.f64 (-.f64 t z) a) x)) 2)

213.0ms

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

27.0ms

(*.f64 (cbrt.f64 (fma.f64 y (/.f64 (-.f64 t z) a) x)) (pow.f64 (cbrt.f64 (fma.f64 y (/.f64 (-.f64 t z) a) x)) 2))

rewrite63.0ms (0.7%)

Algorithm

2×	batch-egg-rewrite

Rules

610×	`prod-diff_binary64`
230×	`expm1-udef_binary64`
230×	`log1p-udef_binary64`
131×	`add-sqr-sqrt_binary64`
125×	`log1p-expm1-u_binary64`

Counts

3 → 60

Calls

3 calls:

61.0ms

(*.f64 (cbrt.f64 (fma.f64 y (/.f64 (-.f64 t z) a) x)) (pow.f64 (cbrt.f64 (fma.f64 y (/.f64 (-.f64 t z) a) x)) 2))

61.0ms

(pow.f64 (cbrt.f64 (fma.f64 y (/.f64 (-.f64 t z) a) x)) 2)

61.0ms

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	40
1	260	38
2	3217	38
3	5120	38
0	0	0
1	0	0

simplify239.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

808×	`fma-def_binary64`
402×	`*-commutative_binary64`
209×	`cancel-sign-sub-inv_binary64`
193×	`sub-neg_binary64`
188×	`+-commutative_binary64`

Counts

240 → 260

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	966	15572
1	3501	15300
2	5143	15300

prune435.0ms (4.9%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	457	0	457
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	457	5	462

Error

0.0b

Counts

462 → 5

Alt Table

Status	Error	Program
	33.3b	(pow.f64 (sqrt.f64 (fma.f64 (-.f64 t z) (/.f64 y a) x)) 2)
✓	7.6b	(*.f64 (cbrt.f64 (fma.f64 y (/.f64 (-.f64 t z) a) x)) (pow.f64 (cbrt.f64 (fma.f64 y (/.f64 (-.f64 t z) a) x)) 2))
✓	6.5b	(fma.f64 y (/.f64 (-.f64 t z) a) x)
▶	7.7b	(-.f64 x (/.f64 (*.f64 y (-.f64 z t)) a))
✓	2.4b	(fma.f64 (-.f64 t z) (/.f64 y a) x)

Compiler

Compiled 30920 to 14176 computations (54.2% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 y (-.f64 z t))
✓	0.0b	(-.f64 x (/.f64 (*.f64 y (-.f64 z t)) a))
✓	8.0b	(/.f64 (*.f64 y (-.f64 z t)) a)

series60.0ms (0.7%)

Counts

3 → 144

Calls

3 calls:

31.0ms	(-.f64 x (/.f64 (*.f64 y (-.f64 z t)) a))
20.0ms	(/.f64 (*.f64 y (-.f64 z t)) a)
8.0ms	(*.f64 y (-.f64 z t))

rewrite98.0ms (1.1%)

Algorithm

2×	batch-egg-rewrite

Rules

946×	`prod-diff_binary64`
214×	`egg-rr`
120×	`add-sqr-sqrt_binary64`
115×	`log1p-expm1-u_binary64`
115×	`expm1-log1p-u_binary64`

Counts

3 → 214

Calls

3 calls:

91.0ms	(*.f64 y (-.f64 z t))
91.0ms	(-.f64 x (/.f64 (*.f64 y (-.f64 z t)) a))
91.0ms	(/.f64 (*.f64 y (-.f64 z t)) a)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	30
1	226	30
2	3236	30
3	5250	30
0	0	0
1	0	0

simplify128.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

784×	`fma-neg_binary64`
364×	`fma-def_binary64`
243×	`cancel-sign-sub-inv_binary64`
122×	`distribute-rgt-in_binary64`
115×	`associate-/l*_binary64`

Counts

358 → 245

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	36	1390
1	88	1390
2	185	1388
3	374	1298
4	744	1298
5	1256	1298
6	1276	1298
7	1404	1298
8	1420	1298
9	1434	1298
10	1438	1298
11	1365	1298

prune358.0ms (4%)

Pruning

7 alts after pruning (3 fresh and 4 done)

	Pruned	Kept	Total
New	243	2	245
Fresh	0	1	1
Picked	0	1	1
Done	0	3	3
Total	243	7	250

Error

Counts

250 → 7

Alt Table

Status	Error	Program
	7.7b	(-.f64 x (pow.f64 (/.f64 a (*.f64 y (-.f64 z t))) -1))
✓	6.5b	(fma.f64 y (/.f64 (-.f64 t z) a) x)
	33.3b	(pow.f64 (sqrt.f64 (fma.f64 (-.f64 t z) (/.f64 y a) x)) 2)
✓	7.6b	(*.f64 (cbrt.f64 (fma.f64 y (/.f64 (-.f64 t z) a) x)) (pow.f64 (cbrt.f64 (fma.f64 y (/.f64 (-.f64 t z) a) x)) 2))
✓	7.7b	(-.f64 x (/.f64 (*.f64 y (-.f64 z t)) a))
	19.7b	(-.f64 x (.f64 (/.f64 1 (cbrt.f64 (.f64 a a))) (/.f64 (*.f64 y (-.f64 z t)) (cbrt.f64 a))))
✓	2.4b	(fma.f64 (-.f64 t z) (/.f64 y a) x)

Compiler

Compiled 7320 to 1790 computations (75.5% saved)

regimes845.0ms (9.4%)

Accuracy

Total 0.3b remaining (94.6%)

Threshold costs 0.3b (94.6%)

Counts

44 → 3

Compiler

Compiled 7281 to 4586 computations (37% saved)

bsearch1.0ms (0%)

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

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	59
1	29	59
2	42	59
3	56	59
4	68	59
5	82	59
6	90	59
7	92	59
8	94	59
9	95	59
10	91	59

end133.0ms (1.5%)

Compiler: Compiled 212 to 114 computations (46.2% saved)

Details

analyze2.4s (26.7%)

sample2.6s (29.1%)

simplify76.0ms (0.8%)

prune6.0ms (0.1%)

localize12.0ms (0.1%)

series115.0ms (1.3%)

rewrite153.0ms (1.7%)

simplify100.0ms (1.1%)

prune152.0ms (1.7%)

localize6.0ms (0.1%)

series51.0ms (0.6%)

rewrite52.0ms (0.6%)

simplify101.0ms (1.1%)

prune18.0ms (0.2%)

localize13.0ms (0.1%)

series733.0ms (8.2%)

rewrite63.0ms (0.7%)

simplify239.0ms (2.7%)

prune435.0ms (4.9%)

localize6.0ms (0.1%)

series60.0ms (0.7%)

rewrite98.0ms (1.1%)

simplify128.0ms (1.4%)

prune358.0ms (4%)

regimes845.0ms (9.4%)

bsearch1.0ms (0%)

simplify7.0ms (0.1%)

end133.0ms (1.5%)

Profiling