Details

analyze180.0ms (5.7%)

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)

sample20.0ms (0.6%)

Algorithm

1×

intervals

Results

12.0ms	256×	body	128	valid
0.0ms	8×	body	128	invalid

Compiler

Compiled 29 to 23 computations (20.7% saved)

simplify78.0ms (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

5.6b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	5.6b	(/.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))
✓	5.2b	(/.f64 (.f64 (-.f64 1 x) (-.f64 3 x)) (.f64 y 3))

series14.0ms (0.5%)

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

simplify89.0ms (2.8%)

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

prune136.0ms (4.3%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	147	7	154
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	148	7	155

Error

0.0b

Counts

155 → 7

Alt Table

Status	Error	Program
	5.5b	(/.f64 (/.f64 (*.f64 (-.f64 1 x) (-.f64 3 x)) y) 3)
	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)))
	5.4b	(/.f64 (-.f64 (+.f64 1 (.f64 1/3 (pow.f64 x 2))) (.f64 4/3 x)) y)
	5.5b	(/.f64 1 (/.f64 (.f64 y 3) (.f64 (-.f64 1 x) (-.f64 3 x))))
▶	0.1b	(*.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 3377 to 2294 computations (32.1% 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))

series23.0ms (0.7%)

Counts

3 → 52

Calls

3 calls:

16.0ms	(*.f64 (/.f64 (-.f64 1 x) y) (/.f64 (-.f64 3 x) 3))
5.0ms	(/.f64 (-.f64 1 x) y)
2.0ms	(/.f64 (-.f64 3 x) 3)

rewrite40.0ms (1.3%)

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:

14.0ms	(*.f64 (/.f64 (-.f64 1 x) y) (/.f64 (-.f64 3 x) 3))
5.0ms	(/.f64 (-.f64 3 x) 3)
5.0ms	(/.f64 (-.f64 1 x) y)

simplify141.0ms (4.5%)

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

prune165.0ms (5.2%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	207	3	210
Fresh	4	2	6
Picked	1	0	1
Done	0	0	0
Total	212	5	217

Error

Counts

217 → 5

Alt Table

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

Compiler

Compiled 4040 to 2912 computations (27.9% 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 (-.f64 1 x) (/.f64 (/.f64 (-.f64 3 x) 3) y))
✓	0.1b	(/.f64 (/.f64 (-.f64 3 x) 3) y)

series20.0ms (0.6%)

Counts

2 → 48

Calls

2 calls:

12.0ms	(*.f64 (-.f64 1 x) (/.f64 (/.f64 (-.f64 3 x) 3) y))
8.0ms	(/.f64 (/.f64 (-.f64 3 x) 3) y)

rewrite47.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

222×	`times-frac_binary64`
160×	`add-sqr-sqrt_binary64`
151×	`*-un-lft-identity_binary64`
106×	`add-cube-cbrt_binary64`
61×	`associate-r_binary64`

Counts

2 → 189

Calls

2 calls:

20.0ms	(*.f64 (-.f64 1 x) (/.f64 (/.f64 (-.f64 3 x) 3) y))
7.0ms	(/.f64 (/.f64 (-.f64 3 x) 3) y)

simplify161.0ms (5.1%)

Algorithm

1×	egg-herbie

Rules

613×	`distribute-rgt-in_binary64`
458×	`div-sub_binary64`
278×	`fma-def_binary64`
190×	`associate-/l/_binary64`
173×	`associate-/l*_binary64`

Counts

237 → 271

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	315	4919
1	779	4646
2	2709	4472
3	4651	4460
4	5492	4460

prune282.0ms (9%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	324	0	324
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	324	5	329

Error

Counts

329 → 5

Alt Table

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

Compiler

Compiled 6783 to 4930 computations (27.3% saved)

localize7.0ms (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 3 x) 3) (/.f64 (-.f64 1 x) y))

series14.0ms (0.4%)

Counts

1 → 24

Calls

1 calls:

14.0ms

(*.f64 (/.f64 (-.f64 3 x) 3) (/.f64 (-.f64 1 x) y))

rewrite22.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

47×	`add-sqr-sqrt_binary64`
37×	`times-frac_binary64`
35×	`*-un-lft-identity_binary64`
22×	`associate-r_binary64`
20×	`add-cube-cbrt_binary64`

Counts

1 → 67

Calls

1 calls:

14.0ms

(*.f64 (/.f64 (-.f64 3 x) 3) (/.f64 (-.f64 1 x) y))

simplify57.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

589×	`associate-*l/_binary64`
481×	`associate-/l*_binary64`
357×	`distribute-rgt-in_binary64`
343×	`distribute-lft-in_binary64`
222×	`associate-/l/_binary64`

Counts

91 → 112

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	154	1926
1	436	1726
2	1404	1700
3	5020	1700

prune177.0ms (5.6%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	218	0	218
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	218	5	223

Error

Counts

223 → 5

Alt Table

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

Compiler

Compiled 4111 to 2999 computations (27% saved)

regimes707.0ms (22.5%)

Accuracy

Total 0.1b remaining (92.5%)

Threshold costs 0.1b (92.5%)

Counts

147 → 1

Compiler

Compiled 11655 to 8949 computations (23.2% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	16
1	16	16
2	21	16
3	23	16
4	24	16
5	23	16

end0.0ms (0%)

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

sample721.0ms (22.9%)

Algorithm

1×

intervals

Results

306.0ms	8000×	body	128	valid
11.0ms	297×	body	128	invalid

Compiler

Compiled 105 to 80 computations (23.8% saved)

Details

analyze180.0ms (5.7%)

sample20.0ms (0.6%)

simplify78.0ms (2.5%)

prune2.0ms (0.1%)

localize6.0ms (0.2%)

series14.0ms (0.5%)

rewrite25.0ms (0.8%)

simplify89.0ms (2.8%)

prune136.0ms (4.3%)

localize6.0ms (0.2%)

series23.0ms (0.7%)

rewrite40.0ms (1.3%)

simplify141.0ms (4.5%)

prune165.0ms (5.2%)

localize6.0ms (0.2%)

series20.0ms (0.6%)

rewrite47.0ms (1.5%)

simplify161.0ms (5.1%)

prune282.0ms (9%)

localize7.0ms (0.2%)

series14.0ms (0.4%)

rewrite22.0ms (0.7%)

simplify57.0ms (1.8%)

prune177.0ms (5.6%)

regimes707.0ms (22.5%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample721.0ms (22.9%)

Profiling