Details

analyze556.0ms (17.5%)

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
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
12.5%	87.4%	0.1%	7
18.7%	81.1%	0.1%	8
31.2%	68.6%	0.1%	9
35.9%	55.4%	8.7%	10
42.9%	47.6%	9.5%	11
51.5%	38.2%	10.3%	12
55%	30%	15%	13
59.5%	25.3%	15.3%	14

Compiler

Compiled 17 to 13 computations (23.5% saved)

sample1.2s (36.7%)

Results

841.0ms	7572×	body	128	valid
93.0ms	284×	body	1024	valid
81.0ms	633×	body	128	invalid
76.0ms	252×	body	512	valid
27.0ms	148×	body	256	valid

Compiler

Compiled 50 to 38 computations (24% saved)

simplify24.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

436×	`unsub-neg_binary64`
376×	`fma-def_binary64`
247×	`distribute-rgt-in_binary64`
216×	`associate-+l+_binary64`
214×	`sub-neg_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	14	16
1	23	14
2	60	14
3	204	12
4	640	12
5	1991	12
6	3879	12

Stop Event

1×	node limit

Counts

1 → 2

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
▶	0.2b	(fma.f64 (-.f64 y x) (fma.f64 z -6 4) x)
	0.8b	(+.f64 x (.f64 (.f64 (-.f64 y x) 6) (-.f64 (/.f64 2 3) z)))

Compiler

Compiled 81 to 56 computations (30.9% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 z -6 4)
✓	0.1b	(fma.f64 (-.f64 y x) (fma.f64 z -6 4) x)

series14.0ms (0.4%)

Counts

2 → 48

Calls

2 calls:

12.0ms	(fma.f64 (-.f64 y x) (fma.f64 z -6 4) x)
1.0ms	(fma.f64 z -6 4)

rewrite41.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

423×	`prod-diff_binary64`
403×	`log-prod_binary64`
204×	`fma-def_binary64`
175×	`expm1-udef_binary64`
175×	`log1p-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	17
1	194	17
2	2401	17

Stop Event

1×	node limit

Counts

2 → 55

Calls

2 calls:

40.0ms	(fma.f64 z -6 4)
40.0ms	(fma.f64 (-.f64 y x) (fma.f64 z -6 4) x)

simplify84.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

1259×	`fma-neg_binary64`
445×	`fma-def_binary64`
153×	`sub-neg_binary64`
122×	`cancel-sign-sub-inv_binary64`
116×	`associate-l_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	40	819
1	121	721
2	316	643
3	760	562
4	1947	562
5	2587	562
6	2877	562
7	2946	562
8	2971	562
9	2973	562
10	4006	562
11	4006	562

Stop Event

1×

saturated

Counts

103 → 75

prune65.0ms (2%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	69	6	75
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	70	7	77

Error

0.0b

Counts

77 → 7

Alt Table

Status	Error	Program
	15.1b	(fma.f64 (-.f64 y x) (expm1.f64 (log1p.f64 (fma.f64 z -6 4))) x)
	0.8b	(+.f64 x (.f64 (.f64 (-.f64 y x) 6) (-.f64 (/.f64 2 3) z)))
	0.2b	(fma.f64 (-.f64 y x) (-.f64 4 (*.f64 6 z)) x)
	37.4b	(.f64 -6 (.f64 z (-.f64 y x)))
▶	0.1b	(fma.f64 x (fma.f64 6 z -3) (*.f64 y (fma.f64 z -6 4)))
	1.2b	(pow.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (fma.f64 z -6 4) x)) 3)
	32.4b	(/.f64 (fma.f64 (.f64 (-.f64 y x) (fma.f64 z -6 4)) (.f64 (-.f64 y x) (fma.f64 z -6 4)) (neg.f64 (*.f64 x x))) (fma.f64 (-.f64 y x) (fma.f64 z -6 4) (neg.f64 x)))

Compiler

Compiled 1247 to 763 computations (38.8% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(fma.f64 z -6 4)
✓	0.0b	(fma.f64 6 z -3)
✓	0.1b	(fma.f64 x (fma.f64 6 z -3) (*.f64 y (fma.f64 z -6 4)))
✓	0.1b	(*.f64 y (fma.f64 z -6 4))

series21.0ms (0.7%)

Counts

3 → 72

Calls

3 calls:

14.0ms	(fma.f64 x (fma.f64 6 z -3) (*.f64 y (fma.f64 z -6 4)))
5.0ms	(*.f64 y (fma.f64 z -6 4))
1.0ms	(fma.f64 6 z -3)

rewrite50.0ms (1.6%)

Algorithm

1×	batch-egg-rewrite

Rules

467×	`log-prod_binary64`
207×	`expm1-udef_binary64`
207×	`log1p-udef_binary64`
187×	`pow3_binary64`
176×	`prod-diff_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	29
1	244	29
2	2665	29

Stop Event

1×	node limit

Counts

3 → 77

Calls

3 calls:

49.0ms	(fma.f64 6 z -3)
49.0ms	(fma.f64 x (fma.f64 6 z -3) (*.f64 y (fma.f64 z -6 4)))
49.0ms	(*.f64 y (fma.f64 z -6 4))

simplify93.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

1255×	`fma-neg_binary64`
441×	`fma-def_binary64`
151×	`sub-neg_binary64`
122×	`cancel-sign-sub-inv_binary64`
118×	`associate-l_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	41	1014
1	122	931
2	316	829
3	757	748
4	1937	748
5	2576	748
6	2857	748
7	2926	748
8	2951	748
9	2953	748
10	3986	748
11	3986	748

Stop Event

1×

saturated

Counts

149 → 100

prune104.0ms (3.3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	130	1	131
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	130	8	138

Error

0.0b

Counts

138 → 8

Alt Table

Status	Error	Program
	15.1b	(fma.f64 (-.f64 y x) (expm1.f64 (log1p.f64 (fma.f64 z -6 4))) x)
	0.8b	(+.f64 x (.f64 (.f64 (-.f64 y x) 6) (-.f64 (/.f64 2 3) z)))
▶	0.2b	(fma.f64 (-.f64 y x) (-.f64 4 (*.f64 6 z)) x)
	37.4b	(.f64 -6 (.f64 z (-.f64 y x)))
	14.6b	(fma.f64 x (cbrt.f64 (pow.f64 (fma.f64 z 6 -3) 3)) (*.f64 y (fma.f64 z -6 4)))
✓	0.1b	(fma.f64 x (fma.f64 6 z -3) (*.f64 y (fma.f64 z -6 4)))
	1.2b	(pow.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (fma.f64 z -6 4) x)) 3)
	32.4b	(/.f64 (fma.f64 (.f64 (-.f64 y x) (fma.f64 z -6 4)) (.f64 (-.f64 y x) (fma.f64 z -6 4)) (neg.f64 (*.f64 x x))) (fma.f64 (-.f64 y x) (fma.f64 z -6 4) (neg.f64 x)))

Compiler

Compiled 2375 to 1709 computations (28% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 4 (*.f64 6 z))
✓	0.1b	(fma.f64 (-.f64 y x) (-.f64 4 (*.f64 6 z)) x)

series13.0ms (0.4%)

Counts

2 → 39

Calls

2 calls:

11.0ms	(fma.f64 (-.f64 y x) (-.f64 4 (*.f64 6 z)) x)
1.0ms	(-.f64 4 (*.f64 6 z))

rewrite44.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

544×	`prod-diff_binary64`
259×	`fma-def_binary64`
206×	`expm1-udef_binary64`
206×	`log1p-udef_binary64`
128×	`fma-neg_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	10	21
1	228	21
2	2980	17

Stop Event

1×	node limit

Counts

2 → 67

Calls

2 calls:

43.0ms	(-.f64 4 (*.f64 6 z))
43.0ms	(fma.f64 (-.f64 y x) (-.f64 4 (*.f64 6 z)) x)

simplify88.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

1259×	`fma-neg_binary64`
445×	`fma-def_binary64`
153×	`sub-neg_binary64`
122×	`cancel-sign-sub-inv_binary64`
116×	`associate-l_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	40	756
1	121	658
2	316	598
3	760	517
4	1947	517
5	2587	517
6	2877	517
7	2946	517
8	2971	517
9	2973	517
10	4006	517
11	4006	517

Stop Event

1×

saturated

Counts

106 → 85

prune58.0ms (1.8%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	85	0	85
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	85	8	93

Error

0.0b

Counts

93 → 8

Alt Table

Status	Error	Program
	15.1b	(fma.f64 (-.f64 y x) (expm1.f64 (log1p.f64 (fma.f64 z -6 4))) x)
▶	0.8b	(+.f64 x (.f64 (.f64 (-.f64 y x) 6) (-.f64 (/.f64 2 3) z)))
✓	0.2b	(fma.f64 (-.f64 y x) (-.f64 4 (*.f64 6 z)) x)
	37.4b	(.f64 -6 (.f64 z (-.f64 y x)))
	14.6b	(fma.f64 x (cbrt.f64 (pow.f64 (fma.f64 z 6 -3) 3)) (*.f64 y (fma.f64 z -6 4)))
✓	0.1b	(fma.f64 x (fma.f64 6 z -3) (*.f64 y (fma.f64 z -6 4)))
	1.2b	(pow.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (fma.f64 z -6 4) x)) 3)
	32.4b	(/.f64 (fma.f64 (.f64 (-.f64 y x) (fma.f64 z -6 4)) (.f64 (-.f64 y x) (fma.f64 z -6 4)) (neg.f64 (*.f64 x x))) (fma.f64 (-.f64 y x) (fma.f64 z -6 4) (neg.f64 x)))

Compiler

Compiled 1411 to 861 computations (39% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (/.f64 2 3) z)
✓	0.0b	(*.f64 (-.f64 y x) 6)
✓	0.2b	(+.f64 x (.f64 (.f64 (-.f64 y x) 6) (-.f64 (/.f64 2 3) z)))
✓	0.4b	(.f64 (.f64 (-.f64 y x) 6) (-.f64 (/.f64 2 3) z))

series33.0ms (1.1%)

Counts

4 → 108

Calls

4 calls:

17.0ms	(+.f64 x (.f64 (.f64 (-.f64 y x) 6) (-.f64 (/.f64 2 3) z)))
11.0ms	(.f64 (.f64 (-.f64 y x) 6) (-.f64 (/.f64 2 3) z))
3.0ms	(*.f64 (-.f64 y x) 6)
1.0ms	(-.f64 (/.f64 2 3) z)

rewrite72.0ms (2.3%)

Algorithm

1×	batch-egg-rewrite

Rules

447×	`fma-def_binary64`
263×	`expm1-udef_binary64`
263×	`log1p-udef_binary64`
214×	`fma-neg_binary64`
146×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	40
1	295	38
2	3858	38

Stop Event

1×	node limit

Counts

4 → 137

Calls

4 calls:

70.0ms	(-.f64 (/.f64 2 3) z)
70.0ms	(*.f64 (-.f64 y x) 6)
70.0ms	(+.f64 x (.f64 (.f64 (-.f64 y x) 6) (-.f64 (/.f64 2 3) z)))
70.0ms	(.f64 (.f64 (-.f64 y x) 6) (-.f64 (/.f64 2 3) z))

simplify68.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

736×	`fma-def_binary64`
456×	`fma-neg_binary64`
279×	`unsub-neg_binary64`
248×	`sub-neg_binary64`
160×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	54	1660
1	157	1577
2	431	1397
3	1079	1208
4	3096	1073
5	4533	1073

Stop Event

1×	node limit

Counts

245 → 169

prune122.0ms (3.8%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	166	3	169
Fresh	4	1	5
Picked	0	1	1
Done	1	1	2
Total	171	6	177

Error

Counts

177 → 6

Alt Table

Status	Error	Program
	0.3b	(fma.f64 6 (*.f64 (-.f64 y x) (-.f64 2/3 z)) x)
	14.6b	(fma.f64 x (cbrt.f64 (pow.f64 (fma.f64 z 6 -3) 3)) (*.f64 y (fma.f64 z -6 4)))
✓	0.8b	(+.f64 x (.f64 (.f64 (-.f64 y x) 6) (-.f64 (/.f64 2 3) z)))
✓	0.1b	(fma.f64 x (fma.f64 6 z -3) (*.f64 y (fma.f64 z -6 4)))
	0.2b	(fma.f64 (*.f64 6 (-.f64 2/3 z)) (-.f64 y x) x)
	32.1b	(fma.f64 (sqrt.f64 x) (sqrt.f64 x) (.f64 (-.f64 y x) (.f64 6 (-.f64 2/3 z))))

Compiler

Compiled 2818 to 1697 computations (39.8% saved)

regimes327.0ms (10.3%)

Accuracy

Total 0.1b remaining (88.3%)

Threshold costs 0.1b (88.3%)

Counts

69 → 1

Compiler

Compiled 5065 to 3666 computations (27.6% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	16
1	13	16

Stop Event

1×

saturated

end96.0ms (3%)

Compiler: Compiled 122 to 88 computations (27.9% saved)

Details

analyze556.0ms (17.5%)

sample1.2s (36.7%)

simplify24.0ms (0.8%)

prune3.0ms (0.1%)

localize6.0ms (0.2%)

series14.0ms (0.4%)

rewrite41.0ms (1.3%)

simplify84.0ms (2.7%)

prune65.0ms (2%)

localize8.0ms (0.2%)

series21.0ms (0.7%)

rewrite50.0ms (1.6%)

simplify93.0ms (2.9%)

prune104.0ms (3.3%)

localize6.0ms (0.2%)

series13.0ms (0.4%)

rewrite44.0ms (1.4%)

simplify88.0ms (2.8%)

prune58.0ms (1.8%)

localize8.0ms (0.2%)

series33.0ms (1.1%)

rewrite72.0ms (2.3%)

simplify68.0ms (2.1%)

prune122.0ms (3.8%)

regimes327.0ms (10.3%)

simplify2.0ms (0.1%)

end96.0ms (3%)

Profiling