Details

analyze130.0ms (3.9%)

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
25%	74.9%	0.1%	5
37.5%	62.4%	0.1%	6
50%	46.8%	3.2%	7
56.2%	37.5%	6.3%	8
62.4%	25.8%	11.8%	9
65.6%	20.3%	14.1%	10
68.7%	13.5%	17.9%	11
70.2%	10.5%	19.2%	12
71.8%	6.9%	21.3%	13
72.6%	5.4%	22%	14

Compiler

Compiled 14 to 11 computations (21.4% saved)

sample65.0ms (2%)

Algorithm

1×

intervals

Results

9.0ms	256×	body	128	valid
1.0ms	14×	body	128	invalid

Compiler

Compiled 29 to 23 computations (20.7% saved)

simplify81.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

877×	`div-sub_binary64`
637×	`sub-neg_binary64`
618×	`unsub-neg_binary64`
440×	`neg-sub0_binary64`
439×	`neg-mul-1_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	16
1	24	16
2	71	16
3	192	16
4	634	16
5	1914	16
6	3304	16
7	4241	16
8	4674	16
9	4931	16

prune2.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	2	3

Error

3.7b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	3.7b	(/.f64 (.f64 (-.f64 1 x) (-.f64 3 x)) (.f64 y 3))

Compiler

Compiled 50 to 38 computations (24% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (-.f64 1 x) (-.f64 3 x))
✓	3.5b	(/.f64 (.f64 (-.f64 1 x) (-.f64 3 x)) (.f64 y 3))

series14.0ms (0.4%)

Counts

2 → 36

Calls

2 calls:

12.0ms	(/.f64 (.f64 (-.f64 1 x) (-.f64 3 x)) (.f64 y 3))
2.0ms	(*.f64 (-.f64 1 x) (-.f64 3 x))

rewrite25.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`add-sqr-sqrt_binary64`
23×	`*-un-lft-identity_binary64`
18×	`prod-diff_binary64`
18×	`add-cube-cbrt_binary64`
16×	`add-cbrt-cube_binary64`

Counts

2 → 90

Calls

2 calls:

11.0ms	(*.f64 (-.f64 1 x) (-.f64 3 x))
9.0ms	(/.f64 (.f64 (-.f64 1 x) (-.f64 3 x)) (.f64 y 3))

simplify83.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

852×	`fma-def_binary64`
614×	`associate-/r*_binary64`
196×	`associate-l_binary64`
194×	`associate-/l/_binary64`
174×	`associate-r_binary64`

Counts

126 → 154

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	215	2319
1	508	2006
2	2204	1772
3	4855	1760
4	4865	1760

prune130.0ms (3.9%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	149	5	154
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	149	6	155

Error

Counts

155 → 6

Alt Table

Status	Error	Program
▶	0.1b	(/.f64 (-.f64 1 x) (/.f64 y (/.f64 (-.f64 3 x) 3)))
	0.2b	(/.f64 (-.f64 1 x) (/.f64 (*.f64 y 3) (-.f64 3 x)))
	3.6b	(/.f64 (+.f64 1 (*.f64 x (fma.f64 1/3 x -4/3))) y)
	0.1b	(*.f64 (/.f64 (-.f64 1 x) y) (/.f64 (-.f64 3 x) 3))
	0.1b	(fma.f64 (/.f64 x y) -4/3 (fma.f64 1/3 (*.f64 (/.f64 x y) x) (/.f64 1 y)))
✓	3.7b	(/.f64 (.f64 (-.f64 1 x) (-.f64 3 x)) (.f64 y 3))

Compiler

Compiled 3328 to 2254 computations (32.3% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 3 x) 3)
✓	0.1b	(/.f64 y (/.f64 (-.f64 3 x) 3))
✓	0.1b	(/.f64 (-.f64 1 x) (/.f64 y (/.f64 (-.f64 3 x) 3)))

series25.0ms (0.8%)

Counts

3 → 60

Calls

3 calls:

14.0ms	(/.f64 (-.f64 1 x) (/.f64 y (/.f64 (-.f64 3 x) 3)))
10.0ms	(/.f64 y (/.f64 (-.f64 3 x) 3))
2.0ms	(/.f64 (-.f64 3 x) 3)

rewrite304.0ms (9.2%)

Algorithm

1×	rewrite-expression-head

Rules

1218×	`times-frac_binary64`
808×	`*-un-lft-identity_binary64`
808×	`add-sqr-sqrt_binary64`
461×	`add-cube-cbrt_binary64`
205×	`difference-of-squares_binary64`

Counts

3 → 598

Calls

3 calls:

20.0ms	(/.f64 (-.f64 1 x) (/.f64 y (/.f64 (-.f64 3 x) 3)))
6.0ms	(/.f64 y (/.f64 (-.f64 3 x) 3))
4.0ms	(/.f64 (-.f64 3 x) 3)

simplify413.0ms (12.5%)

Algorithm

1×	egg-herbie

Rules

554×	`associate-/l/_binary64`
532×	`associate-/r*_binary64`
489×	`associate-/r/_binary64`
395×	`associate-/l*_binary64`
278×	`div-sub_binary64`

Counts

658 → 750

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	740	21081
1	2010	20780
2	5237	20780

prune599.0ms (18.1%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	750	0	750
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	750	6	756

Error

Counts

756 → 6

Alt Table

Status	Error	Program
✓	0.1b	(/.f64 (-.f64 1 x) (/.f64 y (/.f64 (-.f64 3 x) 3)))
	0.2b	(/.f64 (-.f64 1 x) (/.f64 (*.f64 y 3) (-.f64 3 x)))
	3.6b	(/.f64 (+.f64 1 (*.f64 x (fma.f64 1/3 x -4/3))) y)
	0.1b	(*.f64 (/.f64 (-.f64 1 x) y) (/.f64 (-.f64 3 x) 3))
▶	0.1b	(fma.f64 (/.f64 x y) -4/3 (fma.f64 1/3 (*.f64 (/.f64 x y) x) (/.f64 1 y)))
✓	3.7b	(/.f64 (.f64 (-.f64 1 x) (-.f64 3 x)) (.f64 y 3))

Compiler

Compiled 19425 to 13918 computations (28.4% saved)

localize10.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 (/.f64 x y) -4/3 (fma.f64 1/3 (*.f64 (/.f64 x y) x) (/.f64 1 y)))
✓	0.1b	(fma.f64 1/3 (*.f64 (/.f64 x y) x) (/.f64 1 y))
✓	0.2b	(*.f64 (/.f64 x y) x)

series49.0ms (1.5%)

Counts

3 → 72

Calls

3 calls:

19.0ms	(fma.f64 (/.f64 x y) -4/3 (fma.f64 1/3 (*.f64 (/.f64 x y) x) (/.f64 1 y)))
18.0ms	(fma.f64 1/3 (*.f64 (/.f64 x y) x) (/.f64 1 y))
12.0ms	(*.f64 (/.f64 x y) x)

rewrite8.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-sqr-sqrt_binary64`
13×	`associate-l_binary64`
11×	`*-un-lft-identity_binary64`
11×	`add-cube-cbrt_binary64`
10×	`times-frac_binary64`

Counts

3 → 54

Calls

3 calls:

5.0ms	(*.f64 (/.f64 x y) x)
0.0ms	(fma.f64 1/3 (*.f64 (/.f64 x y) x) (/.f64 1 y))
0.0ms	(fma.f64 (/.f64 x y) -4/3 (fma.f64 1/3 (*.f64 (/.f64 x y) x) (/.f64 1 y)))

simplify80.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

580×	`distribute-rgt-in_binary64`
565×	`distribute-lft-in_binary64`
411×	`fma-def_binary64`
269×	`fma-neg_binary64`
234×	`associate-l_binary64`

Counts

126 → 106

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	106	1832
1	228	1631
2	542	1453
3	1758	1356
4	4849	1356
5	4939	1356

prune90.0ms (2.7%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	105	1	106
Fresh	1	2	3
Picked	0	1	1
Done	0	2	2
Total	106	6	112

Error

Counts

112 → 6

Alt Table

Status	Error	Program
✓	0.1b	(/.f64 (-.f64 1 x) (/.f64 y (/.f64 (-.f64 3 x) 3)))
	0.2b	(/.f64 (-.f64 1 x) (/.f64 (*.f64 y 3) (-.f64 3 x)))
▶	0.1b	(*.f64 (/.f64 (-.f64 1 x) y) (/.f64 (-.f64 3 x) 3))
	3.6b	(/.f64 (fma.f64 x (fma.f64 x 1/3 -4/3) 1) y)
✓	0.1b	(fma.f64 (/.f64 x y) -4/3 (fma.f64 1/3 (*.f64 (/.f64 x y) x) (/.f64 1 y)))
✓	3.7b	(/.f64 (.f64 (-.f64 1 x) (-.f64 3 x)) (.f64 y 3))

Compiler

Compiled 2242 to 1084 computations (51.7% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 1 x) y)
	0.0b	(/.f64 (-.f64 3 x) 3)
✓	0.1b	(*.f64 (/.f64 (-.f64 1 x) y) (/.f64 (-.f64 3 x) 3))

series19.0ms (0.6%)

Counts

2 → 40

Calls

2 calls:

13.0ms	(*.f64 (/.f64 (-.f64 1 x) y) (/.f64 (-.f64 3 x) 3))
5.0ms	(/.f64 (-.f64 1 x) y)

rewrite30.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

71×	`add-sqr-sqrt_binary64`
59×	`*-un-lft-identity_binary64`
55×	`times-frac_binary64`
32×	`add-cube-cbrt_binary64`
22×	`associate-l_binary64`

Counts

2 → 111

Calls

2 calls:

17.0ms	(*.f64 (/.f64 (-.f64 1 x) y) (/.f64 (-.f64 3 x) 3))
5.0ms	(/.f64 (-.f64 1 x) y)

simplify76.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

523×	`distribute-rgt-in_binary64`
502×	`distribute-lft-in_binary64`
476×	`times-frac_binary64`
235×	`fma-def_binary64`
146×	`associate-*l/_binary64`

Counts

151 → 156

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	192	2665
1	522	2432
2	1767	2402
3	5327	2402

prune160.0ms (4.8%)

Pruning

6 alts after pruning (2 fresh and 4 done)

	Pruned	Kept	Total
New	209	0	209
Fresh	0	2	2
Picked	0	1	1
Done	0	3	3
Total	209	6	215

Error

Counts

215 → 6

Alt Table

Status	Error	Program
✓	0.1b	(/.f64 (-.f64 1 x) (/.f64 y (/.f64 (-.f64 3 x) 3)))
	0.2b	(/.f64 (-.f64 1 x) (/.f64 (*.f64 y 3) (-.f64 3 x)))
✓	0.1b	(*.f64 (/.f64 (-.f64 1 x) y) (/.f64 (-.f64 3 x) 3))
	3.6b	(/.f64 (fma.f64 x (fma.f64 x 1/3 -4/3) 1) y)
✓	0.1b	(fma.f64 (/.f64 x y) -4/3 (fma.f64 1/3 (*.f64 (/.f64 x y) x) (/.f64 1 y)))
✓	3.7b	(/.f64 (.f64 (-.f64 1 x) (-.f64 3 x)) (.f64 y 3))

Compiler

Compiled 3966 to 2855 computations (28% saved)

regimes270.0ms (8.2%)

Accuracy

Total 0.1b remaining (90.4%)

Threshold costs 0.1b (90.4%)

Counts

54 → 1

Compiler

Compiled 3822 to 2882 computations (24.6% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

3×	`+-commutative_binary64`
3×	`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	10	16
1	15	16
2	20	16
3	22	16
4	23	16
5	22	16

end0.0ms (0%)

Compiler: Compiled 13 to 10 computations (23.1% saved)

sample623.0ms (18.8%)

Algorithm

1×

intervals

Results

317.0ms	8000×	body	128	valid
17.0ms	350×	body	128	invalid

Compiler

Compiled 109 to 81 computations (25.7% saved)

Details

analyze130.0ms (3.9%)

sample65.0ms (2%)

simplify81.0ms (2.4%)

prune2.0ms (0.1%)

localize6.0ms (0.2%)

series14.0ms (0.4%)

rewrite25.0ms (0.8%)

simplify83.0ms (2.5%)

prune130.0ms (3.9%)

localize6.0ms (0.2%)

series25.0ms (0.8%)

rewrite304.0ms (9.2%)

simplify413.0ms (12.5%)

prune599.0ms (18.1%)

localize10.0ms (0.3%)

series49.0ms (1.5%)

rewrite8.0ms (0.2%)

simplify80.0ms (2.4%)

prune90.0ms (2.7%)

localize6.0ms (0.2%)

series19.0ms (0.6%)

rewrite30.0ms (0.9%)

simplify76.0ms (2.3%)

prune160.0ms (4.8%)

regimes270.0ms (8.2%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample623.0ms (18.8%)

Profiling