Details

analyze900.0ms (2.7%)

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
13.3%	86.5%	0.2%	9
17.5%	82.3%	0.2%	10
23.6%	75.2%	1.2%	11
25%	72%	2.9%	12
35.8%	59.6%	4.6%	13
40.3%	54.3%	5.4%	14

Compiler

Compiled 14 to 9 computations (35.7% saved)

sample1.4s (4.1%)

Results

895.0ms	8256×	body	128	valid
251.0ms	2198×	body	128	invalid

Compiler

Compiled 41 to 26 computations (36.6% saved)

simplify68.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

938×	`fma-def_binary64`
721×	`fma-neg_binary64`
220×	`cancel-sign-sub-inv_binary64`
144×	`distribute-rgt-in_binary64`
108×	`div-sub_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	11
1	16	11
2	37	11
3	72	11
4	140	11
5	242	11
6	395	11
7	682	11
8	1049	11
9	1368	11
10	1492	11
11	1530	11
12	1536	11
13	1541	11
14	1541	11
15	1456	11

prune3.0ms (0%)

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

1.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	1.1b	(fma.f64 (/.f64 x y) (-.f64 z t) t)

Compiler

Compiled 45 to 23 computations (48.9% saved)

localize6.0ms (0%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	1.1b	(fma.f64 (/.f64 x y) (-.f64 z t) t)

series15.0ms (0%)

Counts

1 → 48

Calls

1 calls:

15.0ms

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

rewrite48.0ms (0.1%)

Algorithm

2×	batch-egg-rewrite

Rules

455×	`log-prod_binary64`
446×	`prod-diff_binary64`
199×	`fma-def_binary64`
170×	`expm1-udef_binary64`
170×	`log1p-udef_binary64`

Counts

1 → 30

Calls

1 calls:

48.0ms

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	11
1	175	11
2	2373	11
3	5034	11
0	0	0
1	0	0

simplify88.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

704×	`fma-neg_binary64`
624×	`fma-def_binary64`
169×	`cancel-sign-sub-inv_binary64`
155×	`distribute-rgt-in_binary64`
101×	`associate-/l*_binary64`

Counts

78 → 40

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	29	561
1	70	561
2	156	552
3	277	480
4	537	480
5	946	480
6	1286	480
7	1427	480
8	1479	480
9	1530	480
10	1531	480
11	1531	480
12	1446	480

prune23.0ms (0.1%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	35	5	40
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	35	6	41

Error

0.0b

Counts

41 → 6

Alt Table

Status	Error	Program
	38.4b	(cbrt.f64 (pow.f64 (fma.f64 (/.f64 x y) (-.f64 z t) t) 3))
	34.2b	(pow.f64 (sqrt.f64 (fma.f64 (/.f64 x y) (-.f64 z t) t)) 2)
▶	2.3b	(pow.f64 (cbrt.f64 (fma.f64 (/.f64 x y) (-.f64 z t) t)) 3)
✓	1.1b	(fma.f64 (/.f64 x y) (-.f64 z t) t)
	36.3b	(*.f64 x (/.f64 (-.f64 z t) y))
	6.8b	(-.f64 (+.f64 t (/.f64 (.f64 z x) y)) (/.f64 (.f64 t x) y))

Compiler

Compiled 678 to 224 computations (67% saved)

localize8.0ms (0%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.5b	(cbrt.f64 (fma.f64 (/.f64 x y) (-.f64 z t) t))
✓	0.7b	(pow.f64 (cbrt.f64 (fma.f64 (/.f64 x y) (-.f64 z t) t)) 3)
	1.1b	(fma.f64 (/.f64 x y) (-.f64 z t) t)

series26.5s (79.7%)

Counts

2 → 96

Calls

2 calls:

26.4s	(pow.f64 (cbrt.f64 (fma.f64 (/.f64 x y) (-.f64 z t) t)) 3)
82.0ms	(cbrt.f64 (fma.f64 (/.f64 x y) (-.f64 z t) t))

rewrite84.0ms (0.3%)

Algorithm

2×	batch-egg-rewrite

Rules

537×	`prod-diff_binary64`
209×	`fma-def_binary64`
199×	`expm1-udef_binary64`
199×	`log1p-udef_binary64`
177×	`log-pow_binary64`

Counts

2 → 69

Calls

2 calls:

82.0ms	(cbrt.f64 (fma.f64 (/.f64 x y) (-.f64 z t) t))
82.0ms	(pow.f64 (cbrt.f64 (fma.f64 (/.f64 x y) (-.f64 z t) t)) 3)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	24
1	222	24
2	2796	24
3	4867	24
4	5030	24
0	0	0
1	0	0

simplify109.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

709×	`times-frac_binary64`
471×	`associate-/l*_binary64`
428×	`associate-/r*_binary64`
344×	`fma-def_binary64`
176×	`*-commutative_binary64`

Counts

165 → 181

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	476	7525
1	1697	7308
2	5231	7308

prune157.0ms (0.5%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	219	2	221
Fresh	3	1	4
Picked	0	1	1
Done	0	1	1
Total	222	5	227

Error

0.0b

Counts

227 → 5

Alt Table

Status	Error	Program
	32.6b	(fma.f64 (*.f64 (/.f64 x y) (sqrt.f64 (-.f64 z t))) (sqrt.f64 (-.f64 z t)) t)
	6.8b	(-.f64 (+.f64 t (/.f64 (.f64 z x) y)) (/.f64 (.f64 t x) y))
✓	2.3b	(pow.f64 (cbrt.f64 (fma.f64 (/.f64 x y) (-.f64 z t) t)) 3)
✓	1.1b	(fma.f64 (/.f64 x y) (-.f64 z t) t)
▶	5.4b	(fma.f64 x (*.f64 (/.f64 1 y) (-.f64 z t)) t)

Compiler

Compiled 9295 to 4399 computations (52.7% saved)

localize7.0ms (0%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.3b	(*.f64 (/.f64 1 y) (-.f64 z t))
✓	5.0b	(fma.f64 x (*.f64 (/.f64 1 y) (-.f64 z t)) t)

series27.0ms (0.1%)

Counts

2 → 84

Calls

2 calls:

18.0ms	(fma.f64 x (*.f64 (/.f64 1 y) (-.f64 z t)) t)
9.0ms	(*.f64 (/.f64 1 y) (-.f64 z t))

rewrite57.0ms (0.2%)

Algorithm

2×	batch-egg-rewrite

Rules

498×	`log-prod_binary64`
442×	`prod-diff_binary64`
205×	`fma-def_binary64`
188×	`expm1-udef_binary64`
188×	`log1p-udef_binary64`

Counts

2 → 76

Calls

2 calls:

55.0ms	(*.f64 (/.f64 1 y) (-.f64 z t))
55.0ms	(fma.f64 x (*.f64 (/.f64 1 y) (-.f64 z t)) t)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	18
1	209	18
2	2599	18
3	5329	18
0	0	0
1	0	0

simplify89.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

742×	`fma-def_binary64`
668×	`fma-neg_binary64`
179×	`cancel-sign-sub-inv_binary64`
136×	`distribute-rgt-in_binary64`
116×	`unsub-neg_binary64`

Counts

160 → 91

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	35	792
1	84	792
2	184	720
3	325	720
4	649	720
5	1104	720
6	1410	720
7	1516	720
8	1538	720
9	1539	720
10	1539	720
11	1454	720

prune59.0ms (0.2%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	90	1	91
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	90	6	96

Error

Counts

96 → 6

Alt Table

Status	Error	Program
	32.6b	(fma.f64 (*.f64 (/.f64 x y) (sqrt.f64 (-.f64 z t))) (sqrt.f64 (-.f64 z t)) t)
	6.8b	(-.f64 (+.f64 t (/.f64 (.f64 z x) y)) (/.f64 (.f64 t x) y))
✓	2.3b	(pow.f64 (cbrt.f64 (fma.f64 (/.f64 x y) (-.f64 z t) t)) 3)
✓	1.1b	(fma.f64 (/.f64 x y) (-.f64 z t) t)
✓	5.4b	(fma.f64 x (*.f64 (/.f64 1 y) (-.f64 z t)) t)
▶	5.8b	(fma.f64 x (pow.f64 (cbrt.f64 (/.f64 (-.f64 z t) y)) 3) t)

Compiler

Compiled 1373 to 465 computations (66.1% saved)

localize9.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 z t) y)
✓	0.7b	(pow.f64 (cbrt.f64 (/.f64 (-.f64 z t) y)) 3)
✓	5.0b	(fma.f64 x (pow.f64 (cbrt.f64 (/.f64 (-.f64 z t) y)) 3) t)
✓	7.5b	(cbrt.f64 (/.f64 (-.f64 z t) y))

series2.6s (7.8%)

Counts

4 → 148

Calls

4 calls:

1.4s	(pow.f64 (cbrt.f64 (/.f64 (-.f64 z t) y)) 3)
1.0s	(fma.f64 x (pow.f64 (cbrt.f64 (/.f64 (-.f64 z t) y)) 3) t)
201.0ms	(cbrt.f64 (/.f64 (-.f64 z t) y))
10.0ms	(/.f64 (-.f64 z t) y)

rewrite150.0ms (0.5%)

Algorithm

2×	batch-egg-rewrite

Rules

615×	`prod-diff_binary64`
468×	`fma-udef_binary64`
302×	`fma-def_binary64`
296×	`egg-rr`
211×	`fma-neg_binary64`

Counts

4 → 296

Calls

4 calls:

142.0ms	(/.f64 (-.f64 z t) y)
142.0ms	(pow.f64 (cbrt.f64 (/.f64 (-.f64 z t) y)) 3)
142.0ms	(fma.f64 x (pow.f64 (cbrt.f64 (/.f64 (-.f64 z t) y)) 3) t)
142.0ms	(cbrt.f64 (/.f64 (-.f64 z t) y))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	34
1	226	34
2	2942	34
3	4889	34
4	4815	34
5	5000	34
0	0	0
1	0	0

simplify129.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

985×	`times-frac_binary64`
567×	`fma-def_binary64`
228×	`fma-neg_binary64`
176×	`associate-r_binary64`
174×	`sub-neg_binary64`

Counts

444 → 306

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	240	4188
1	726	4071
2	2501	3837
3	4936	3837
4	4992	3837

prune197.0ms (0.6%)

Pruning

6 alts after pruning (2 fresh and 4 done)

	Pruned	Kept	Total
New	306	0	306
Fresh	0	2	2
Picked	0	1	1
Done	0	3	3
Total	306	6	312

Error

Counts

312 → 6

Alt Table

Status	Error	Program
	32.6b	(fma.f64 (*.f64 (/.f64 x y) (sqrt.f64 (-.f64 z t))) (sqrt.f64 (-.f64 z t)) t)
	6.8b	(-.f64 (+.f64 t (/.f64 (.f64 z x) y)) (/.f64 (.f64 t x) y))
✓	2.3b	(pow.f64 (cbrt.f64 (fma.f64 (/.f64 x y) (-.f64 z t) t)) 3)
✓	1.1b	(fma.f64 (/.f64 x y) (-.f64 z t) t)
✓	5.4b	(fma.f64 x (*.f64 (/.f64 1 y) (-.f64 z t)) t)
✓	5.8b	(fma.f64 x (pow.f64 (cbrt.f64 (/.f64 (-.f64 z t) y)) 3) t)

Compiler

Compiled 7307 to 3151 computations (56.9% saved)

regimes464.0ms (1.4%)

Accuracy

Total 1.8b remaining (98.8%)

Threshold costs 0b (0%)

Counts

81 → 1

Compiler

Compiled 6926 to 4396 computations (36.5% saved)

simplify3.0ms (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	8	11
1	10	11
2	15	11
3	17	11
4	18	11
5	18	11

end78.0ms (0.2%)

Compiler: Compiled 115 to 69 computations (40% saved)

Details

analyze900.0ms (2.7%)

sample1.4s (4.1%)

simplify68.0ms (0.2%)

prune3.0ms (0%)

localize6.0ms (0%)

series15.0ms (0%)

rewrite48.0ms (0.1%)

simplify88.0ms (0.3%)

prune23.0ms (0.1%)

localize8.0ms (0%)

series26.5s (79.7%)

rewrite84.0ms (0.3%)

simplify109.0ms (0.3%)

prune157.0ms (0.5%)

localize7.0ms (0%)

series27.0ms (0.1%)

rewrite57.0ms (0.2%)

simplify89.0ms (0.3%)

prune59.0ms (0.2%)

localize9.0ms (0%)

series2.6s (7.8%)

rewrite150.0ms (0.5%)

simplify129.0ms (0.4%)

prune197.0ms (0.6%)

regimes464.0ms (1.4%)

simplify3.0ms (0%)

end78.0ms (0.2%)

Profiling