Details

analyze847.0ms (21.6%)

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
43.3%	48%	8.7%	10
49.7%	40.8%	9.5%	11
55.7%	34%	10.3%	12
61.3%	23.7%	15%	13
65%	19.8%	15.3%	14

Compiler

Compiled 13 to 9 computations (30.8% saved)

sample39.0ms (1%)

Algorithm

1×

intervals

Results

19.0ms	256×	body	128	valid
2.0ms	25×	body	128	invalid

Compiler

Compiled 28 to 20 computations (28.6% saved)

simplify62.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

782×	`fma-def_binary64`
523×	`fma-neg_binary64`
142×	`cancel-sign-sub-inv_binary64`
122×	`distribute-rgt-in_binary64`
106×	`unsub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	16	11
2	36	11
3	78	11
4	154	11
5	268	11
6	404	11
7	631	11
8	911	11
9	1092	11
10	1291	11
11	1314	11
12	1316	11
13	1316	11
14	1243	11

prune6.0ms (0.2%)

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

0.2b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.2b	(fma.f64 (*.f64 (-.f64 y x) 6) z x)
	0.2b	(+.f64 x (.f64 (.f64 (-.f64 y x) 6) z))

Compiler

Compiled 66 to 41 computations (37.9% saved)

localize11.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (-.f64 y x) 6)
✓	0.2b	(fma.f64 (*.f64 (-.f64 y x) 6) z x)

series28.0ms (0.7%)

Counts

2 → 60

Calls

2 calls:

20.0ms	(fma.f64 (*.f64 (-.f64 y x) 6) z x)
7.0ms	(*.f64 (-.f64 y x) 6)

rewrite15.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`add-sqr-sqrt_binary64`
6×	`*-un-lft-identity_binary64`
5×	`associate-l_binary64`
4×	`add-cube-cbrt_binary64`
4×	`add-cbrt-cube_binary64`

Counts

2 → 34

Calls

2 calls:

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

simplify129.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

829×	`times-frac_binary64`
732×	`fma-def_binary64`
490×	`unsub-neg_binary64`
306×	`*-commutative_binary64`
289×	`neg-sub0_binary64`

Counts

94 → 70

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	85	1108
1	190	899
2	520	893
3	1543	893
4	3149	893
5	4667	893
6	6079	893

prune117.0ms (3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	64	6	70
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	65	7	72

Error

0.0b

Counts

72 → 7

Alt Table

Status	Error	Program
▶	0.2b	(fma.f64 6 (*.f64 z (-.f64 y x)) x)
	32.5b	(fma.f64 (.f64 (sqrt.f64 (-.f64 y x)) (.f64 (sqrt.f64 (-.f64 y x)) 6)) z x)
	0.8b	(fma.f64 (.f64 (.f64 (cbrt.f64 (.f64 (-.f64 y x) 6)) (cbrt.f64 (.f64 (-.f64 y x) 6))) (cbrt.f64 (*.f64 (-.f64 y x) 6))) z x)
✓	0.2b	(fma.f64 (*.f64 (-.f64 y x) 6) z x)
	0.2b	(+.f64 (.f64 6 (.f64 z (-.f64 y x))) x)
	1.4b	(.f64 (.f64 (cbrt.f64 (fma.f64 (.f64 (-.f64 y x) 6) z x)) (cbrt.f64 (fma.f64 (.f64 (-.f64 y x) 6) z x))) (cbrt.f64 (fma.f64 (*.f64 (-.f64 y x) 6) z x)))
	26.3b	(fma.f64 x (*.f64 z -6) x)

Compiler

Compiled 1107 to 548 computations (50.5% saved)

localize16.0ms (0.4%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 z (-.f64 y x))
✓	0.2b	(fma.f64 6 (*.f64 z (-.f64 y x)) x)

series34.0ms (0.9%)

Counts

2 → 60

Calls

2 calls:

20.0ms	(fma.f64 6 (*.f64 z (-.f64 y x)) x)
14.0ms	(*.f64 z (-.f64 y x))

rewrite22.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`add-sqr-sqrt_binary64`
20×	`*-un-lft-identity_binary64`
18×	`prod-diff_binary64`
18×	`add-cube-cbrt_binary64`
13×	`distribute-lft-in_binary64`

Counts

2 → 60

Calls

2 calls:

13.0ms	(*.f64 z (-.f64 y x))
1.0ms	(fma.f64 6 (*.f64 z (-.f64 y x)) x)

simplify173.0ms (4.4%)

Algorithm

1×	egg-herbie

Rules

708×	`fma-neg_binary64`
433×	`exp-prod_binary64`
341×	`fma-def_binary64`
283×	`neg-mul-1_binary64`
228×	`*-commutative_binary64`

Counts

120 → 90

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	146	1596
1	271	1231
2	838	1171
3	2033	1117
4	3701	1117
5	4979	1117
6	4994	1117
7	4789	1117

prune110.0ms (2.8%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	89	1	90
Fresh	3	2	5
Picked	0	1	1
Done	0	1	1
Total	92	5	97

Error

Counts

97 → 5

Alt Table

Status	Error	Program
✓	0.2b	(fma.f64 6 (*.f64 z (-.f64 y x)) x)
	32.5b	(fma.f64 (.f64 (sqrt.f64 (-.f64 y x)) (.f64 (sqrt.f64 (-.f64 y x)) 6)) z x)
✓	0.2b	(fma.f64 (*.f64 (-.f64 y x) 6) z x)
	0.2b	(+.f64 (.f64 6 (.f64 z (-.f64 y x))) x)
▶	0.2b	(fma.f64 (*.f64 6 z) (-.f64 y x) x)

Compiler

Compiled 1570 to 588 computations (62.5% saved)

localize14.0ms (0.4%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.2b	(fma.f64 (*.f64 6 z) (-.f64 y x) x)

series19.0ms (0.5%)

Counts

1 → 36

Calls

1 calls:

19.0ms

(fma.f64 (*.f64 6 z) (-.f64 y x) x)

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

1×	`*-un-lft-identity_binary64`
1×	`add-sqr-sqrt_binary64`
1×	`add-cube-cbrt_binary64`
1×	`add-cbrt-cube_binary64`
1×	`add-exp-log_binary64`

Counts

1 → 10

Calls

1 calls:

1.0ms

(fma.f64 (*.f64 6 z) (-.f64 y x) x)

simplify84.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

743×	`distribute-rgt-neg-out_binary64`
441×	`associate-l_binary64`
426×	`distribute-rgt-in_binary64`
414×	`distribute-lft-in_binary64`
395×	`associate-r_binary64`

Counts

46 → 29

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	39	697
1	100	512
2	221	506
3	586	506
4	2785	506
5	5027	506

prune29.0ms (0.8%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	29	0	29
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	29	5	34

Error

Counts

34 → 5

Alt Table

Status	Error	Program
✓	0.2b	(fma.f64 6 (*.f64 z (-.f64 y x)) x)
	32.5b	(fma.f64 (.f64 (sqrt.f64 (-.f64 y x)) (.f64 (sqrt.f64 (-.f64 y x)) 6)) z x)
✓	0.2b	(fma.f64 (*.f64 (-.f64 y x) 6) z x)
▶	0.2b	(+.f64 (.f64 6 (.f64 z (-.f64 y x))) x)
✓	0.2b	(fma.f64 (*.f64 6 z) (-.f64 y x) x)

Compiler

Compiled 429 to 217 computations (49.4% saved)

localize13.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (.f64 6 (.f64 z (-.f64 y x))) x)
	0.0b	(*.f64 z (-.f64 y x))
✓	0.3b	(.f64 6 (.f64 z (-.f64 y x)))

series42.0ms (1.1%)

Counts

2 → 64

Calls

2 calls:

24.0ms	(+.f64 (.f64 6 (.f64 z (-.f64 y x))) x)
17.0ms	(.f64 6 (.f64 z (-.f64 y x)))

rewrite77.0ms (2%)

Algorithm

1×	rewrite-expression-head

Rules

104×	`distribute-lft-in_binary64`
104×	`distribute-rgt-in_binary64`
72×	`prod-diff_binary64`
59×	`*-un-lft-identity_binary64`
59×	`add-sqr-sqrt_binary64`

Counts

2 → 140

Calls

2 calls:

22.0ms	(+.f64 (.f64 6 (.f64 z (-.f64 y x))) x)
15.0ms	(.f64 6 (.f64 z (-.f64 y x)))

simplify225.0ms (5.7%)

Algorithm

1×	egg-herbie

Rules

820×	`fma-def_binary64`
646×	`fma-neg_binary64`
499×	`*-commutative_binary64`
443×	`distribute-rgt-in_binary64`
414×	`distribute-lft-in_binary64`

Counts

204 → 207

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	256	2963
1	388	2592
2	1250	2154
3	3956	2154
4	4926	2154
5	4902	2154

prune318.0ms (8.1%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	267	1	268
Fresh	1	0	1
Picked	0	1	1
Done	0	3	3
Total	268	5	273

Error

Counts

273 → 5

Alt Table

Status	Error	Program
✓	0.2b	(fma.f64 (*.f64 (-.f64 y x) 6) z x)
✓	0.2b	(+.f64 (.f64 6 (.f64 z (-.f64 y x))) x)
	0.6b	(+.f64 (.f64 (sqrt.f64 6) (.f64 (sqrt.f64 6) (*.f64 z (-.f64 y x)))) x)
✓	0.2b	(fma.f64 (*.f64 6 z) (-.f64 y x) x)
✓	0.2b	(fma.f64 6 (*.f64 z (-.f64 y x)) x)

Compiler

Compiled 5993 to 2114 computations (64.7% saved)

regimes239.0ms (6.1%)

Accuracy

Total 0.2b remaining (96.6%)

Threshold costs 0.2b (96.6%)

Counts

34 → 1

Compiler

Compiled 1744 to 1154 computations (33.8% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	11
1	11	11
2	16	11
3	18	11
4	19	11
5	19	11

end1.0ms (0%)

Compiler: Compiled 11 to 7 computations (36.4% saved)

sample1.2s (31.7%)

Algorithm

1×

intervals

Results

575.0ms	8000×	body	128	valid
45.0ms	629×	body	128	invalid

Compiler

Compiled 88 to 60 computations (31.8% saved)

Details

analyze847.0ms (21.6%)

sample39.0ms (1%)

simplify62.0ms (1.6%)

prune6.0ms (0.2%)

localize11.0ms (0.3%)

series28.0ms (0.7%)

rewrite15.0ms (0.4%)

simplify129.0ms (3.3%)

prune117.0ms (3%)

localize16.0ms (0.4%)

series34.0ms (0.9%)

rewrite22.0ms (0.6%)

simplify173.0ms (4.4%)

prune110.0ms (2.8%)

localize14.0ms (0.4%)

series19.0ms (0.5%)

rewrite1.0ms (0%)

simplify84.0ms (2.1%)

prune29.0ms (0.8%)

localize13.0ms (0.3%)

series42.0ms (1.1%)

rewrite77.0ms (2%)

simplify225.0ms (5.7%)

prune318.0ms (8.1%)

regimes239.0ms (6.1%)

simplify5.0ms (0.1%)

end1.0ms (0%)

sample1.2s (31.7%)

Profiling