Details

analyze332.0ms (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
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)

sample33.0ms (0.5%)

Algorithm

1×

intervals

Results

18.0ms	256×	body	128	valid
0.0ms	7×	body	128	invalid

Compiler

Compiled 29 to 23 computations (20.7% saved)

simplify93.0ms (1.4%)

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

prune4.0ms (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

6.2b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	6.2b	(/.f64 (.f64 (-.f64 1 x) (-.f64 3 x)) (.f64 y 3))

Compiler

Compiled 50 to 38 computations (24% saved)

localize12.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (-.f64 1 x) (-.f64 3 x))
✓	5.8b	(/.f64 (.f64 (-.f64 1 x) (-.f64 3 x)) (.f64 y 3))

series32.0ms (0.5%)

Counts

2 → 36

Calls

2 calls:

28.0ms	(/.f64 (.f64 (-.f64 1 x) (-.f64 3 x)) (.f64 y 3))
4.0ms	(*.f64 (-.f64 1 x) (-.f64 3 x))

rewrite52.0ms (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:

21.0ms	(/.f64 (.f64 (-.f64 1 x) (-.f64 3 x)) (.f64 y 3))
17.0ms	(*.f64 (-.f64 1 x) (-.f64 3 x))

simplify169.0ms (2.6%)

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

prune277.0ms (4.2%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	149	5	154
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	150	5	155

Error

0.0b

Counts

155 → 5

Alt Table

Status	Error	Program
▶	0.1b	(/.f64 (-.f64 1 x) (/.f64 y (/.f64 (-.f64 3 x) 3)))
	0.5b	(/.f64 (-.f64 1 x) (/.f64 (*.f64 y 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)))
	0.2b	(*.f64 (/.f64 (-.f64 1 x) y) (/.f64 (-.f64 3 x) 3))
	6.2b	(/.f64 (-.f64 (+.f64 3 (pow.f64 x 2)) (.f64 4 x)) (.f64 y 3))

Compiler

Compiled 3321 to 2250 computations (32.2% saved)

localize14.0ms (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)))

series57.0ms (0.9%)

Counts

3 → 60

Calls

3 calls:

34.0ms	(/.f64 (-.f64 1 x) (/.f64 y (/.f64 (-.f64 3 x) 3)))
20.0ms	(/.f64 y (/.f64 (-.f64 3 x) 3))
3.0ms	(/.f64 (-.f64 3 x) 3)

rewrite282.0ms (4.3%)

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:

39.0ms	(/.f64 (-.f64 1 x) (/.f64 y (/.f64 (-.f64 3 x) 3)))
15.0ms	(/.f64 y (/.f64 (-.f64 3 x) 3))
9.0ms	(/.f64 (-.f64 3 x) 3)

simplify792.0ms (12%)

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

prune863.0ms (13.1%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	747	3	750
Fresh	2	2	4
Picked	1	0	1
Done	0	0	0
Total	750	5	755

Error

Counts

755 → 5

Alt Table

Status	Error	Program
▶	0.2b	(*.f64 (/.f64 (-.f64 1 x) y) (/.f64 (-.f64 3 x) 3))
	0.2b	(/.f64 (-.f64 1 x) (*.f64 3 (/.f64 y (-.f64 3 x))))
	6.1b	(/.f64 (-.f64 (fma.f64 1/3 (.f64 x x) 1) (.f64 4/3 x)) y)
	0.2b	(/.f64 (-.f64 1 x) (/.f64 1 (/.f64 (/.f64 (-.f64 3 x) 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 19433 to 13924 computations (28.3% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

series39.0ms (0.6%)

Counts

2 → 40

Calls

2 calls:

27.0ms	(*.f64 (/.f64 (-.f64 1 x) y) (/.f64 (-.f64 3 x) 3))
12.0ms	(/.f64 (-.f64 1 x) y)

rewrite61.0ms (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:

32.0ms	(*.f64 (/.f64 (-.f64 1 x) y) (/.f64 (-.f64 3 x) 3))
10.0ms	(/.f64 (-.f64 1 x) y)

simplify157.0ms (2.4%)

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

prune289.0ms (4.4%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	208	1	209
Fresh	2	2	4
Picked	0	1	1
Done	0	0	0
Total	210	4	214

Error

Counts

214 → 4

Alt Table

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

Compiler

Compiled 3985 to 2867 computations (28.1% saved)

localize12.0ms (0.2%)

Local error

Found 3 expressions with local error:

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

series46.0ms (0.7%)

Counts

2 → 48

Calls

2 calls:

33.0ms	(*.f64 (-.f64 1 x) (/.f64 (/.f64 (-.f64 3 x) 3) y))
13.0ms	(/.f64 (/.f64 (-.f64 3 x) 3) y)

rewrite94.0ms (1.4%)

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:

35.0ms	(*.f64 (-.f64 1 x) (/.f64 (/.f64 (-.f64 3 x) 3) y))
16.0ms	(/.f64 (/.f64 (-.f64 3 x) 3) y)

simplify203.0ms (3.1%)

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 → 273

Iterations

Useful iterations: 3 (0.0ms)

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

prune318.0ms (4.8%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	326	0	326
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	326	4	330

Error

Counts

330 → 4

Alt Table

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

Compiler

Compiled 6728 to 4887 computations (27.4% saved)

regimes1.2s (18.3%)

Accuracy

Total 0.1b remaining (89.4%)

Threshold costs 0.1b (89.4%)

Counts

156 → 1

Compiler

Compiled 12491 to 9645 computations (22.8% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	16
1	17	16
2	25	16
3	29	16
4	31	16
5	30	16

end1.0ms (0%)

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

sample1.1s (17.3%)

Algorithm

1×

intervals

Results

606.0ms	8000×	body	128	valid
21.0ms	296×	body	128	invalid

Compiler

Compiled 85 to 63 computations (25.9% saved)

Details

analyze332.0ms (5%)

sample33.0ms (0.5%)

simplify93.0ms (1.4%)

prune4.0ms (0.1%)

localize12.0ms (0.2%)

series32.0ms (0.5%)

rewrite52.0ms (0.8%)

simplify169.0ms (2.6%)

prune277.0ms (4.2%)

localize14.0ms (0.2%)

series57.0ms (0.9%)

rewrite282.0ms (4.3%)

simplify792.0ms (12%)

prune863.0ms (13.1%)

localize9.0ms (0.1%)

series39.0ms (0.6%)

rewrite61.0ms (0.9%)

simplify157.0ms (2.4%)

prune289.0ms (4.4%)

localize12.0ms (0.2%)

series46.0ms (0.7%)

rewrite94.0ms (1.4%)

simplify203.0ms (3.1%)

prune318.0ms (4.8%)

regimes1.2s (18.3%)

simplify5.0ms (0.1%)

end1.0ms (0%)

sample1.1s (17.3%)

Profiling