Details

analyze128.0ms (3.8%)

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)

sample64.0ms (1.9%)

Algorithm

1×

intervals

Results

10.0ms	256×	body	128	valid
0.0ms	9×	body	128	invalid

Compiler

Compiled 29 to 23 computations (20.7% saved)

simplify84.0ms (2.5%)

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

4.6b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	4.6b	(/.f64 (.f64 (-.f64 1 x) (-.f64 3 x)) (.f64 y 3))

Compiler

Compiled 50 to 38 computations (24% saved)

localize7.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (-.f64 1 x) (-.f64 3 x))
✓	4.3b	(/.f64 (.f64 (-.f64 1 x) (-.f64 3 x)) (.f64 y 3))

series15.0ms (0.4%)

Counts

2 → 36

Calls

2 calls:

13.0ms	(/.f64 (.f64 (-.f64 1 x) (-.f64 3 x)) (.f64 y 3))
2.0ms	(*.f64 (-.f64 1 x) (-.f64 3 x))

rewrite27.0ms (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))
10.0ms	(/.f64 (.f64 (-.f64 1 x) (-.f64 3 x)) (.f64 y 3))

simplify91.0ms (2.7%)

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

prune135.0ms (4%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	148	6	154
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	149	6	155

Error

Counts

155 → 6

Alt Table

Status	Error	Program
	0.2b	(/.f64 (-.f64 1 x) (/.f64 (*.f64 y 3) (-.f64 3 x)))
	11.8b	(/.f64 (.f64 (-.f64 (.f64 1 1) (.f64 x x)) (-.f64 3 x)) (.f64 y (fma.f64 x 3 3)))
	4.7b	(.f64 (.f64 (-.f64 1 x) (-.f64 3 x)) (/.f64 1 (*.f64 y 3)))
	4.4b	(/.f64 (+.f64 1 (*.f64 x (fma.f64 1/3 x -4/3))) y)
▶	0.2b	(*.f64 (/.f64 (-.f64 1 x) y) (/.f64 (-.f64 3 x) 3))
	0.2b	(fma.f64 (/.f64 x y) -4/3 (fma.f64 1/3 (*.f64 (/.f64 x y) x) (/.f64 1 y)))

Compiler

Compiled 3359 to 2278 computations (32.2% 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)
✓	0.2b	(*.f64 (/.f64 (-.f64 1 x) y) (/.f64 (-.f64 3 x) 3))

series26.0ms (0.8%)

Counts

3 → 52

Calls

3 calls:

19.0ms	(*.f64 (/.f64 (-.f64 1 x) y) (/.f64 (-.f64 3 x) 3))
6.0ms	(/.f64 (-.f64 1 x) y)
2.0ms	(/.f64 (-.f64 3 x) 3)

rewrite38.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

90×	`add-sqr-sqrt_binary64`
78×	`*-un-lft-identity_binary64`
70×	`times-frac_binary64`
43×	`add-cube-cbrt_binary64`
22×	`associate-l_binary64`

Counts

3 → 151

Calls

3 calls:

16.0ms	(*.f64 (/.f64 (-.f64 1 x) y) (/.f64 (-.f64 3 x) 3))
5.0ms	(/.f64 (-.f64 1 x) y)
5.0ms	(/.f64 (-.f64 3 x) 3)

simplify134.0ms (4%)

Algorithm

1×	egg-herbie

Rules

539×	`distribute-rgt-in_binary64`
490×	`times-frac_binary64`
284×	`fma-def_binary64`
153×	`associate-*r/_binary64`
150×	`associate-*l/_binary64`

Counts

203 → 210

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	228	3302
1	602	3033
2	1953	2971
3	4746	2959
4	4996	2959
5	4946	2959

prune158.0ms (4.7%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	209	1	210
Fresh	1	4	5
Picked	1	0	1
Done	0	0	0
Total	211	5	216

Error

Counts

216 → 5

Alt Table

Status	Error	Program
▶	0.1b	(*.f64 (/.f64 (-.f64 1 x) y) (/.f64 1 (/.f64 3 (-.f64 3 x))))
	0.2b	(/.f64 (-.f64 1 x) (/.f64 (*.f64 y 3) (-.f64 3 x)))
	4.7b	(.f64 (.f64 (-.f64 1 x) (-.f64 3 x)) (/.f64 1 (*.f64 y 3)))
	4.4b	(/.f64 (+.f64 1 (*.f64 x (fma.f64 1/3 x -4/3))) y)
	0.2b	(fma.f64 (/.f64 x y) -4/3 (fma.f64 1/3 (*.f64 (/.f64 x y) x) (/.f64 1 y)))

Compiler

Compiled 4032 to 2904 computations (28% saved)

localize7.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series17.0ms (0.5%)

Counts

3 → 48

Calls

3 calls:

13.0ms	(*.f64 (/.f64 (-.f64 1 x) y) (/.f64 1 (/.f64 3 (-.f64 3 x))))
3.0ms	(/.f64 3 (-.f64 3 x))
2.0ms	(/.f64 1 (/.f64 3 (-.f64 3 x)))

rewrite77.0ms (2.3%)

Algorithm

1×	rewrite-expression-head

Rules

281×	`times-frac_binary64`
222×	`add-sqr-sqrt_binary64`
193×	`*-un-lft-identity_binary64`
130×	`add-cube-cbrt_binary64`
68×	`associate-r_binary64`

Counts

3 → 284

Calls

3 calls:

33.0ms	(*.f64 (/.f64 (-.f64 1 x) y) (/.f64 1 (/.f64 3 (-.f64 3 x))))
7.0ms	(/.f64 1 (/.f64 3 (-.f64 3 x)))
4.0ms	(/.f64 3 (-.f64 3 x))

simplify192.0ms (5.7%)

Algorithm

1×	egg-herbie

Rules

549×	`times-frac_binary64`
543×	`distribute-rgt-in_binary64`
287×	`fma-def_binary64`
255×	`fma-neg_binary64`
194×	`*-commutative_binary64`

Counts

332 → 423

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	289	6137
1	723	5594
2	2298	5303
3	4779	5291
4	4937	5291

prune444.0ms (13.1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	475	1	476
Fresh	1	3	4
Picked	0	1	1
Done	0	0	0
Total	476	5	481

Error

Counts

481 → 5

Alt Table

Status	Error	Program
✓	0.1b	(*.f64 (/.f64 (-.f64 1 x) y) (/.f64 1 (/.f64 3 (-.f64 3 x))))
	4.7b	(.f64 (.f64 (-.f64 1 x) (-.f64 3 x)) (/.f64 1 (*.f64 y 3)))
	4.4b	(/.f64 (+.f64 1 (*.f64 x (fma.f64 1/3 x -4/3))) y)
▶	0.1b	(/.f64 (.f64 (-.f64 1 x) 1) (.f64 y (/.f64 3 (-.f64 3 x))))
	0.2b	(fma.f64 (/.f64 x y) -4/3 (fma.f64 1/3 (*.f64 (/.f64 x y) x) (/.f64 1 y)))

Compiler

Compiled 10732 to 8405 computations (21.7% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

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

series28.0ms (0.8%)

Counts

2 → 48

Calls

2 calls:

15.0ms	(/.f64 (.f64 (-.f64 1 x) 1) (.f64 y (/.f64 3 (-.f64 3 x))))
13.0ms	(*.f64 y (/.f64 3 (-.f64 3 x)))

rewrite26.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

37×	`add-exp-log_binary64`
28×	`add-cbrt-cube_binary64`
23×	`add-sqr-sqrt_binary64`
21×	`associate-r_binary64`
18×	`*-un-lft-identity_binary64`

Counts

2 → 75

Calls

2 calls:

10.0ms	(/.f64 (.f64 (-.f64 1 x) 1) (.f64 y (/.f64 3 (-.f64 3 x))))
8.0ms	(*.f64 y (/.f64 3 (-.f64 3 x)))

simplify120.0ms (3.5%)

Algorithm

1×	egg-herbie

Rules

576×	`associate-/r/_binary64`
463×	`fma-def_binary64`
293×	`distribute-rgt-in_binary64`
260×	`distribute-lft-in_binary64`
210×	`fma-neg_binary64`

Counts

123 → 134

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	203	2232
1	522	1897
2	2131	1840
3	4715	1828
4	4983	1828
5	4999	1828
6	4939	1828

prune356.0ms (10.5%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	192	0	192
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	192	5	197

Error

Counts

197 → 5

Alt Table

Status	Error	Program
✓	0.1b	(*.f64 (/.f64 (-.f64 1 x) y) (/.f64 1 (/.f64 3 (-.f64 3 x))))
	4.7b	(.f64 (.f64 (-.f64 1 x) (-.f64 3 x)) (/.f64 1 (*.f64 y 3)))
	4.4b	(/.f64 (+.f64 1 (*.f64 x (fma.f64 1/3 x -4/3))) y)
✓	0.1b	(/.f64 (.f64 (-.f64 1 x) 1) (.f64 y (/.f64 3 (-.f64 3 x))))
	0.2b	(fma.f64 (/.f64 x y) -4/3 (fma.f64 1/3 (*.f64 (/.f64 x y) x) (/.f64 1 y)))

Compiler

Compiled 3882 to 2966 computations (23.6% saved)

regimes510.0ms (15.1%)

Accuracy

Total 0.1b remaining (87.8%)

Threshold costs 0.1b (87.8%)

Counts

93 → 1

Compiler

Compiled 7055 to 5435 computations (23% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

3×	`+-commutative_binary64`
3×	`*-commutative_binary64`
3×	`sub-neg_binary64`
1×	`*-rgt-identity_binary64`
1×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	16
1	18	16
2	23	16
3	25	16
4	26	16
5	25	16

end0.0ms (0%)

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

sample682.0ms (20.2%)

Algorithm

1×

intervals

Results

363.0ms	8000×	body	128	valid
13.0ms	333×	body	128	invalid

Compiler

Compiled 103 to 78 computations (24.3% saved)

Details

analyze128.0ms (3.8%)

sample64.0ms (1.9%)

simplify84.0ms (2.5%)

prune2.0ms (0.1%)

localize7.0ms (0.2%)

series15.0ms (0.4%)

rewrite27.0ms (0.8%)

simplify91.0ms (2.7%)

prune135.0ms (4%)

localize6.0ms (0.2%)

series26.0ms (0.8%)

rewrite38.0ms (1.1%)

simplify134.0ms (4%)

prune158.0ms (4.7%)

localize7.0ms (0.2%)

series17.0ms (0.5%)

rewrite77.0ms (2.3%)

simplify192.0ms (5.7%)

prune444.0ms (13.1%)

localize8.0ms (0.2%)

series28.0ms (0.8%)

rewrite26.0ms (0.8%)

simplify120.0ms (3.5%)

prune356.0ms (10.5%)

regimes510.0ms (15.1%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample682.0ms (20.2%)

Profiling